Ghostbusters/WMG

Ghostbuster tech is Magic-Powered Pseudoscience
Even when people disbelieve in the ghosts; it should be easy enough to prove that their equipment does stuff. Each Ghostbuster wears an "unlicensed nuclear accelerator" on their back that can clearly and undoubtedly send out a stream of energy capable of intense physical damage. ....yet nobody else in their world seems capable of, or even interested in duplicating this technology. This is because they can't. It only works because Egon and Ray believe it works. (Peter and Winston don't care how it works, just that it does, so they don't interfere with the effect.) Any attempts to reproduce this effect would either just fizzle or explode.
 * Fridge Brilliance: Egon and Ray were the first ones to use the packs. Peter didn't use his until he saw they evidently worked.
 * This also explains the constant untried prototyping where "one mistake could cause all life to explode at the speed of light" never happens...and when they cross the streams, it fortunately is always in a situation where something else happens anyways. It also conveniently doesn't hurt people when it hits them in the game, or heck, when they fire it in their general area without the convenience of a lead radiation shield.
 * An alternate explanation is that most people simply aren't crazy enough to strap what equates to a mini-nuke to their backs without anything more substantial than the promise that "it probably won't blow you to New Jersey, we think".
 * I know I wouldn't. The threat of ending up in New Jersey is too high.

The Stay Puft Marshmallow Company suffered a hit to its publicity due to its affiliation with an Eldritch Abomination
Alternatively, it's new slogan became 'Now with 100% less world-destroying demon!'
 * That's not a guess, it happened, and they sued the Ghostbusters for it.

Ghosts are required to keep Psychokinetic Energy (PKE) down. Trapping them unbalances the supernatural "ecosystem."

 * The Ghostbusters start capturing a few traditional, not too dangerous hauntings, and suddenly the PKE meter goes off the scale. This is because regular hauntings actually use up the PKE in an area. Removing minor ghosts concentrates the PKE and allows for a "cross-dimensional rip" event, such as Gozer or even a super-powered ghost like Vigo to come into being. Fortunately the events required to deal with them knocks PKE down to acceptable levels again.
 * Rest assured that whatever city the Rookie gets sent to will have a Cross Dimensional Rip soon after him setting up business.
 * Would that make it an "ectosystem"?
 * This theory, unfortunately, would require a rearranging of the timeline. Dana Barrett gets her first visitation from Gozer and his/her/its minions before the Ghostbusters start catching ghosts. In fact, she's quite explicitly referred to as their first client. Therefore, the presence of Gozer on Earth couldn't be explained by the Ghostbusters' actions. He/she/it was already here.
 * Easily explained; Dana had visions. Things Gozer would want to happen. This happens all the time, in fact, it's why Peter didn't find any readings in Dana's apartment when he checked. Had the PKE not accumulated, this is all it would have been; the echoes of a god in another dimension; barely a blip on the radar.

Vinz and Zuul are Punch Clock Villains
Neither seem particularly malicious (at least after they've possessed human hosts), and both seem fairly amicable and friendly. Vinz seems more like an excited puppy, intrigued by the human world and gushing excitedly about having destroyed previous inhabitants of earth. Zuul, on the other hand, was willing to sleep with Venkman as soon as he gave a (to us) very obvious lie about being affiliated with the Keymaster. Neither do anything significant or malicious between waiting to find each other (which Zuul takes no steps toward achieving other than waiting in bed for Vinz). It's possible that both very simply don't understand how humans work, and are just going about their jobs and are excited by the prospect of sleeping with each other.

Gozer massively depowered himself by taking the form of the Stay-Puft Marshmallow Man.
Stay-Puft is the same thing in the Ghostbuster world as the Pillsbury Doughboy or SpongeBob SquarePants is in ours. A world-wide symbol that children send positive emotions to. As the second movie proves, positive energy has a massive effect on ectoplasmic entities. Gozer was able to counter the massive energy sink and continue operating it as a projected Avatar; but it took a metric buttload to do so. Such that it was rather slow for a Giant Monster; it was beaten by just reversing the gate it came in through; and was outmatched by the villain in Ghostbusters the Video Game.
 * This explains why it seemed to become more monstrous as the public became aware of how dangerous it was. With less goodwill towards the cute image, Gozer's true nature was able to shine through. Presumably, it'd look a lot worse and be much stronger after wrecking New York.
 * I like that idea. Stay-Puft did seem to be getting more aggressive and evil as it continued (both as the city's fear increased, and as it drew closer to the portal), culminating in its fiery, outright demonic incarnation once the proton packs ignited it. And in that case, Ray's choice might have helped saved the city: by thinking of the most harmless thing he could come up with, he slowed Gozer down enough for them to think of a plan.
 * As Venkman said, "Nice thinking, Ray."

Walter Peck really is a Gozer worshipper
Remember he had a high PKE level in the Museum, even after he was slimed to remove possessors. The reason
 * In alternative, Walter Peck was so dumb he never figured out that, and his high PKE level was only due to the fact that he was an ass-kisser. Literally.

Oscar Barrett will have a big part in Ghostbusters 3, if it gets made.
Let's look at the facts - Mother was possesed by a fairly major demon, and he himself was nearly the vessel of an evil wizardy dude. He must have some sort of PKE madness running in his system. If the timeline of the movie remains constant, Oscar would be in his early twenties, the perfect age to strap on a proton pack.

Humans are required for Gozarians to use their powers.
This is more or less stated by Gozer itself when it demands the humans choose its new destructor form at the end of the first movie. The Gozerian pantheon, while powerful, cannot use more than the most basic of their abilities without a human will to shape them. When it first appeared, Gozer made sure to show off to the Ghostbusters without killing them because it wanted their panicked minds to create a powerful form for it. This had some interesting results.
 * Shandor's cult knew this and used it to make deals with them for power after death. Once elevated, Shandor's ghost, being a sane human remnant, was able to channel his new powers well enough to destroy Gozer after absorbing enough PKE. His line "I have chosen" was him actually creating his Destructor form on his own and reveling in his superiority over the Gozer.
 * It always seemed to me that the reason Gozer has to let the inhabitants of the world it's invading select the form in which it attacks them is some rule the thing lives by, either set by itself out of sportsmanship or love of challenge, or else set by some yet higher being or cosmic law. Perhaps it even has to be the first inhabitant(s) to encounter the thing, hence it demanding from the Ghostbusters alone that they make the selection. Had Ray refused any selection like the others, it may have done something to coerce them, like torture them magically, maybe with that same force lightning-like effect.

Ghostbusters takes place in the same universe as Hellboy
Egon states that Ivo Shandor began plotting to summon Gozer to destroy the world shortly after World War One. Professor Broom states that World War Two was just the public face of the "Occult Wars" that began shortly after the First World War. During this time, Grigori Rasputin (yes, THAT Rasputin) began plotting to summon the Ogdru Jahad to destroy the world. Both of them failed, but were eventually succeeded in their efforts. Were Shandor & Rasputin working together? Do the Ghostbusters become B.P.R.D. contractors, similar to Blackwater?

Ghostbusters takes place in the same universe as Men in Black
After the first movie, the entire city undergoes a mass neuralization and most of the records of the Gozer incident destroyed; while there may be whispers and glimpses of what really happened, nobody remembers, and so they believe the official explanation (whatever that might be), and continue to think the Ghostbusters are frauds. After the second movie, the MIB realized they'd have to keep doing this over and over if they didn't do something, so they simply allowed the paranormal to become public knowledge while narrowing their purview to merely the extraterrestrial. However, this order came down after Walter Peck was neuralyzed.
 * Alternatively, they only erased people's memories of the Gozer incident, as Gozer is not a ghost. Also note how, if I remember correctly, Winston is the only character to reference Gozer in the sequel. (They probably allowed the Ghostbusters to remember some or all of the event, in case their knowledge and abilities are needed once more; Louis remembers possibly because being possessed while being partially conscious burns the experience into your soul or something.) It just so happens that by taking away their biggest and most public event, the majority of people assumed all the little events (which have now dropped dramatically after Gozer's defeat) had a logical explanation. For the game, everyone has been deneuralized of the event.
 * Quick, someone turn this into a crossover fic!
 * If someone calls the Ghostbusters mistaking an alien for a ghost, MIB shows up on the scene, neuralizes the Ghostbusters and persons who reported the alien, and everyone is nonethewiser. Also, proton packs = alien science?
 * Aren't both movie franchises owned by Sony Pictures? Also, who would handle a ghost alien? I would imagine a more benign one would be better suited for the MIB (who are better at negotiations), whereas the opposite would be handled by the Ghostbusters (presumably ghost physics are universal). However, what if a completely corporeal, non-deific entity from another dimension comes to us? It's not a ghost or deity or anything, but does the MIB extend to inter-dimensional relations?
 * This would probably make sense if you consider the original MIB comic in which they also faced supernatural beings.

The "ghosts" are not actual ghosts.
The Mood Slime reacts to thoughts and emotions, and shapes itself accordingly. All the ghosts, gods and monsters seen were drawn from the minds of those exposed to the ectoplasm.

The "Rookie" name tag was just a placeholder until the rookie could get the custom-ordered tag that bore his actual name.
Presumably, the other Ghostbusters wouldn't have referred to him by name until the custom tag arrived, and the tag didn't arrive until they had defeated Ivo Shandor's plan.

Ghostbusters 3 will end with the Ghostbusters facing off with, and losing to, Heraclitus.
They won't be able to cross the streams. World ends.

Gozer was responsible for the Bronze Age Collapse.
The Bronze Age Collapse was a period of about 100 years between 1250 and 1150 BC during which nearly every major civilization of the ancient Near East was destroyed by some unknown cause. Some archaeologists chalk it up to Earthquakes, Volcanoes, Drought, or War. Those are kind of correct. The ancient Hittites summoned Gozer the Destructor and s/he annihilated civilization.

Looking directly into the trap has it steal your "soul".
"Soul" as in emotions (or some emotions, based on how long you look at it).

In the films, the only times Egon really shows any emotions is during a deleted scene when they are getting kicked out of the University (he grabs Venkman), which was prior to the trapping, and when he gets mad at Peck (clearly, his soul or some such was released when all the ghosts escaped, or the sudden surge of psychokinetic energy affected his behaviour).

Similarly, some experiment (perhaps designing an early trap) prior to the first film did something to Venkman's soul, hence why he can look into the trap and why he never takes anything seriously.

Guesses on where the next office will be.

 * Philadelphia - An old city with many haunted locations, especially the infamous Eastern State Pentitentiary, whose spirits are already reported as violent.
 * Washington, D.C. - Since the Busters are recognized by the state of New York, the Federal government could call them to clean up many of their buildings and properties
 * Chicago - With the Hull House and Ressurection Cemetary, the new office will already have a who's who of supernatural beings.
 * Charleston, SC - As the third oldest surviving city in the US, there are more than enough famous ghosts for the Ghostbusters to deal with, from Anabelle Lee to Edward "Blackbeard" Teach.
 * Memphis, TN - Depending on the timing, you could have Slimer rock out with the ghosts of Elvis Presley, Jerry Lee Lewis, and Isaac Hayes.
 * Boston, MA - Right in the heart of Lovecraft Country.
 * Bangor, ME - Smack dab in the middle of Stephen King Country
 * St. Louis, MO - Home of the infamous Lemp Mansion and Brewery, whose history of suicide and corruption has surely boosted the city's psychic turbulence.
 * Seattle, WA - At least seven documented ghosts just in the Pike Place Market, clear on the opposite coast (they are lacking in West Coast presence), and attracted an unfortunate amount of infamous serial killers.

Walter Peck is a Sin-Eater
This could explain why he had such a high PKE level in the video game after he was no longer possessed. He died in the first movie after being buried under marshmallow and was brought back. The PKE meter was able to detect his Geist even after it had fused with him.

Willow Rosenberg from Buffy the Vampire Slayer is Egon's niece
They're (maybe) both Jewish, (Egon Ambiguously so, Willow in an Informed kind of way) and we can assume Badass Bookworm is an inherited trait. In the video game Egon mentions a niece, and he's given a brother in the first movie novelization. Scientists and scholars run in Egon's family. Throw in some continuity from the cartoon, and the Spenglers have a couple of wizards in their family tree as well.

So Willow is Egon's brother's daughter. Okay, so that leaves her with the wrong last name... but I could see her mom as the type to insist on keeping (and possibly passing down) her own surname name due to ideas on psychology/sociology/patriarchy/proper parenting.

Oscar is the Destructor.
The Stay Puft Man was a decoy put on by Gozer to distract the city and confuse the Ghostbusters. The true choosers of the form were Vinz and Zuul, who chose a human form by possessing Louis and Dana then unlocking the gate with the key. Notice how, after the Gozer temple is destroyed, Dana and Louis become perfectly encases in easily-escaped shells that conveniently shielded them from the blast. Gozer did this on purpose.

Since it involved incubating a powerful cosmic entity, the initial stages of Dana's pregnancy took years instead of weeks. Fortunately, she had a husband to attribute the pregnancy to at the time when it became more apparent. Oscar's presumably strong spiritual presence is what attracted the pink slime in the beginning of Ghostbusters II, even before Vigo chose him as his vessel.

The chosen Gozer-greeters for the Vuldruni and the Shubs and/or Zuuls chose their own versions of the Stay-Puft Marshmallow Man.
Gozer appeared as a giant Slor, and a large and moving Torg. I'm guessing a slor is a type of small lizard that were kept as pets in the time of the Meketrex supplicants, and a torg is similar to a hibiscus plant.
 * Disproved by the game, but only by a little bit: from the game, we know that a juvenile giant slor is pretty damn big. It must get even bigger when it matures to adulthood.

The updated logo wasn't the first to be suggested
Since it's intended as a Take That against the authorities who shut them down, Venkman's original suggestion had the ghost giving the one-digit salute.

Vinz Clortho used to be a normal person
This is why he arguably seems more "human" than Zuul, and also quite possibly more insane. He was actually some other dimension's champion who attempted to fight Gozer, and to give him an eternal punishment Gozer transformed him into one of its heralds. Between being subjected to a glimpse of Gozer's true power and being forced to help destroy world after world, Vinz steadily lost sanity points, until he became the rambling, incoherent thing we see, who even then tries to find what good he can in Gozer's coming. "All prisoners will be released!"

Vinz Clortho is the demon dog equivalent of a socially akward nerd
when Dana gets possessed by Zuul she acts incredibly evil and demonic just as you'd expect, when Lewis gets possessed by Vinz Clortho, he acts twice as goofy and dimwitted, also notice Vinz scenes before the possession, how many times has he stumbled into something, or crashed into something or some other sight gag, he has demonic aspergers

Zuul the demon dog that possesses Dana has a Species Surname
the species that we call demon dogs are called the Zuuls? proof? "many shubs and zuuls knew what it was like to be roasted in the belly of a sloar that day"
 * What if Vinz, having been driven hopelessly insane as suggested above, can only think of the term "women" in the singular example of Zuul, the only (presumably) female he knows. Yes, extradimensional female, but with the whole Gatekeeper thing, I think it holds. When he tries to say "many men and women (or women and children, for that matter) knew what it was like..." it comes out as we might hear a child say "many mommies and daddies."

The demon dogs take on some traits of the person they possess
Zuul changes into a sexy dress, while as a dog doesn't normally wear clothes, most probably doesn't understand the principle of sexyness, and doesn't need it in the first place (the Keymaster's coming anyway). Vinz on the other hand possesses a nerd and becomes a nerd himself.

The pink slime controls Vigo, not the other way around.
We see the pink slime provoking paranormal activity all over town, but Vigo never states that he's in league with other supernatural forces, and his plan seems to be resuming a human reign over the world once he has Oscar's body, which wouldn't make sense if he had an army of ghostly monsters that could betray and kill him once he was made mortal again. Maybe Vigo is just arrogant and, being in a painting, has no clue what's going on outside the museum. The slime just re-animated the spirit within the painting, like it's been doing across the city.

Venkman's experiment at the beginning of Ghostbusters was actually working, and the "mood slime" in Ghostbusters II comes from human waste.

 * Venkman was doing an experiment to test the effects of negative reinforcement on psychic ability. By the end of the experiment, the male subject has enough psychic ability to know that one of the cards has wavy lines on it though not the exact number of lines. This is despite the cards up to this point having geometric shapes rather than abstract "wavy lines". Venkman, preoccupied with sexual conquest, ignores him in favor of the female subject.
 * In Ghostbusters II, Egon is working on a similar experiment - testing how positive and negative feelings affect the environment. It seems to be succeeding as he is seeing spikes of energy in the atmosphere with both positive and negative feelings produced by his human subjects.
 * When the Ghosbusters discover a slime that responds to those positive and negative feelings, even going so far as to stir up psychokinetic energy in the courtroom strong enough to attract ghosts, they believe the slime is the cause of psychic disturbances in the city. In the video game, the slime is explained as bile of a Sloar, but what if that's only part of it? The massive amounts of slime and the fact that it's found in the sewers of New York imply that it didn't come from just one source. It could have built up as an element of human excrement over many years. The experiments of Venkman and Egon proved that humans have both psychic ability influenced outside factors as well as the innate ability to turn it into energy. Of course, human excrement would contain some of this energy.

Egon, and only Egon, is a Time Lord
Ever-popular meme done to death, I know, but I've put a bit of thought into this. Egon is a Chameleon Arched Time Lord who has lost his fob-watch and will never find it again. This is why we know so little about his background other than "[his] parents didn't believe in toys"--all his memories are facts and figures imposed upon him by the Arch. Ray and Peter simply dismiss his more unusual character aspects to his upbringing. His knowledge, advanced WAY beyond our realm, is the product of all his years at the Academy. As for the Ghostbusters technology, there is a "fork in the road" here: either he had a TARDIS and used it to build the Ecto-Containment Unit and other tech, or his level of knowledge is just that deep. He is especially adept at constructing high-tech equipment from common/household objects, another defining trait of renegade Time Lords. (This is doubly so for the Video Game, where the guys have seemingly anachronistic technology for 1991.) But the clincher is, in a way, Walter Peck. Peck is not an EPA agent, but a Celestial Intervention Agent sent to deal with Egon once the 'Busters really hit the big time (his manner is atypical for EPA agents, as discussed in other WM Gs). After all, that knowledge can be very destructive if applied in just the right way. Unfortunately, Venkman doesn't take him seriously, and neither do the other guys (the trick only works on people who are normally cowed by authority figures). Peck fails and his superiors exile him to Earth, where he becomes an incompetent Inspector Javert figure to the Ghostbusters.

The ghosts in the containment unit will disintegrate over time

 * This one overlaps with a lot of other ghost stories, including Kingdom Hospital. In Kingdom, Mary states that Paul, her nemesis, sometimes goes back into the sensory-deprivation tank (presumably where he died) to "recharge". In other words, he must periodically return to the scene of his death to regain PKE. Therefore, the purpose of the Ecto-Containment Unit is to prevent ghosts from returning to the scene of their death and rebuilding their strength. After a while, they begin to disintegrate...at least in theory. Problem is, the G Bs can't put their trophies into separate cells, and there's nothing they can do to stop the ghosts from pooling their collective energies. This is why the ECU in The Real Ghostbusters resembles an alternate dimension: so much ghost energy concentrated in one place.

Ghostbusters 3 will take place on or be released in 2016

 * Remember the other guest on Venkman's show in 2? The one who said it'd end on Valentine's Day? That's a good guess on when it'll finally come around.

Ghostbusters takes place after the events of Madoka Magica.
With now out the door as a universe energy source,  turned toward PKE. So one of them telepathically gave that morose architect the blueprints for the Gozer-summoning building, and another projected the image of Vigo into that one painter's mind.

On another, crueler note, the ghosts seen in Part 1 are actually Witches.

 * Gozer took advantage of the damage done to the spirit/mortal world boundary, with an assist from that building that basically drilled a tunnel into our world.