Star Trek: The Next Generation/Fridge

Fridge Horror

In second season "Where Silence Has No Lease" Picard and Riker set the Enterprise to self destruct in 20 minutes. They avoid it in the end, but you can imagine all the traumatized parents and kids as they awaited their doom... for 20 minutes.
A civilization, knowing death was imminent sends out a probe with memories and stories of their lives up to the end, in the form of a scientists life. Picard experiences a fundamentally altering experience, one that he has good reasons to be emotionally uncomfortable with. But he never tells anyone. An entire civilization died and Picard, an archeologist even, and the only one who knows their story. The hopes of an entire people who get the best possible person to tell their story, and those dreams die with Picard being uncomfortable about his feelings.
- To be fair, he's a starship captain and it's a tv show. He is incredibly busy and we don't get to see everything that goes on. For all we can tell, he's been writing Caimin's memoires throughout the entire series after his experience. The only hint we get that he hasn't done anything is his conversation with Lieutenant Darrin, and that can be explained by him not publishing much yet. If you personally retcon that one, there's no reason to think he hasn't told their story. It's not like the dying wish of a civilization is pertinent to the show outside of that one episode. He could have written the whole story and published it without it ever being mentioned again on the show.
  - He not only published, he got a movie deal. "The Inner Light" was part of it.
At the end of "Ship In A Bottle", Moriarty is left to spend his days in a computer simulation. Nice for him, but from Voyager we know that if you leave a holodeck program running continuously it'll develop glitches and eventually fail. So either Moriarty will think he's going insane as the universe and his beloved start to break down... or he'll realise he's still stuck in a computer, except this time with absolutely no way to escape or even to call for help.
- It gets worse. While its possible that they might have transfered the portable-holodeck to Federation researchers to study, they never seemed to bother trying to remove his program from the Enterprise in all the years since it was first created. So, we're left with the very real possibility that it may have been in the Stardrive section in Generations, meaning Moriarty would have been destroyed along with the Enterprise-D. The other possibility is that he was in the Saucer section and wasn't salvaged, left among the debris on Veridian III and making his final fate even more dreadful.
- Hell, Moriarty's description that even though his program wasn't running, he nonetheless had brief, terrifying moments of disembodied consciousness. That this could even apply to any hologram who had discovered the artificial nature of their reality, such as Cyrus Redblock, the people of Fairhaven, and so forth, the implications become downright terrifying.

"Computer, End Program"

In "Brothers", Noonien Soong, Data's creator, summons him to a planet and tells him the Data has "found his father". However, Soong doesn't act like a father, for reasons not the least of which was subverting Data's will to summon him, instead of simply calling him. He also states that he was only interested in the challenge of creating an artilect. Poor Data (and Lore) had an abusive father.

Fridge Logic

In the episode "The Mind's Eye", the Romulans kidnap Geordi and make him a Manchurian Agent to sabotage Federation/Klingon relations. Their plan is making it look like the Enterprise is supplying rebels on a Klingon planet in civil war. Part of their plan, and a minor test to ensure Geordi's effectiveness, is killing Chief O'Brien. In Ten Forward. The most public area on the ship. Did they seriously think nothing might happen to Geordi afterwards? In fact, when Geordi went to Ten Forward as per the plan, Commander Riker was sitting in plain view! "Luckily", Geordi decides to "accidentally" spill a drink on O'Brien instead. The Romulan's Evil Plan may nearly have backfired because of this minor detail.
- Maybe I'm remembering wrong, but I thought the first time it was just a simulation where he does kill O'Brien and the second time around it was on the real Enterprise and the audience is supposed to be tricked into thinking he was going to kill O'Brien when in fact he never intended to. They already knew they could make him kill one of his friends and think nothing of it through the simulation, so now he was moving on to the actual target.
- Exactly. The test was simply getting Geordi to obey their orders without question, even if they were against what Geordi would do in reality. Then by coincidence, Geordi finds himself in almost the exact same situation in the real world.
In "Q Who", Q did the Federation a back-handed favor. According to that episode, "Q Who" was the first contact with the Borg. However, it later turned out that the NX-01 Enterprise (Episode, "Regeneration") had met the Borg more than a century earlier, and even managed to signal to the Borg of that time about Earth's location. Captain Archer notes that it will take about 200 years for the Borg to receive the signal, or about the time of "The Best of Both Worlds". Q's little trick was to let the Federation know about the Borg before the invasion, giving them some time to prepare. Picard said as much at the end of "Q Who", not knowing that he had just met up with a Borg cube that was already on its way to slurp the Federation down like a milkshake. Or maybe Q was trying to protect Picard, knowing that without some fore-warning, nobody on the Enterprise-D would be able to rescue the Captain.
When Fajo wants to capture Data for his collection, he creates a problem by poisoning a planet's water supply in a way where the Enterprise has to buy hitritium from him in order to counteract it. And hitritium can only be transported ship-to-ship by shuttlecraft. So Fajo arranged things in such a way that he knew somebody from the Enterprise would need to fly a shuttle over to his ship and make himself vulnerable. But how did Fajo know that Data would be assigned to fly the shuttlecraft? Without that tremendous stroke of luck, wouldn't all of his effort have been for nothing?

Fridge Brilliance

This one belongs to SF Debris. In "Hide and Q," First-Season Picard quotes Hamlet without irony about how awesome humans are. Q vanishes in a huff. The next time we see him, he introduces Picard to the Borg, and that ultimately resulted in Picard's hate-filled rant in Star Trek: First Contact. Who's laughing now?
Why do the Borg always go after humanity with a single vessel (or a time travel plot, or a long range indirect missile) rather than just sending twenty cubes in to make sure the job gets done right? Because the Borg don't care a whit about humanity. They stated in "Dark Frontier" that humanity is inferior in almost every way to the majority of species out there. However, they do care about Q. Q protected humans against the Borg before, in the events of "Q Who". The Borg have since then been trying to force Q's hand into interfering again since they desperately want to study and assimilate this semi-omnipotent being. However, the Borg know that they are outclassed against Q and thus don't want to risk half the collective on the effort. Thus, the Borg send in one ship at a time and do increasingly convoluted things to assimilate Earth, all for the sake of getting Q's attention again. Q is fully aware of this, and while he knows what he is doing with regards to the Borg, his son, q, does not, leading to Q's warning: "DON'T PROVOKE THE BORG!"
- When you think about it, the Enterprise's meeting the Borg that first time set off a path that led to the Borg's eventual defeat. A Xanatos Gambit by Q to remove the only thing that might possibly be a threat to the Continuum?
There's been a great deal of head-scratching about the Treaty of Algeron, which prevents the Federation from developing cloaking technology while allowing the Romulans to keep it -- why would the Federation would accept such an unequal treaty? Until you realize that, as of Star Trek II, Starfleet can wipe out planets. (Yes, I'm sure they say they stopped working on the technology, but who would believe that?) Given that it only takes one Genesis torpedo to destroy a world, the combination of cloaked ships and the Genesis device would allow one to commit instant genocide on every other power. Algeron wasn't a treaty with the Romulans, it was a treaty with the rest of the civilized galaxy to prevent them from engaging in a terrified preemptive war on the Federation. Presumably, the treaty likewise prevents the Romulans (and the Klingons, etc.) from attempting to recreate Genesis.
- This also explains why the Romulans and Klingons are never seen using their cloak/warp/decloak/fire/cloak/warp hit and runs with Photon Torpedos (multi-megaton explosives) against planets. They don't want to provoke the federation into retaliating.
I always wondered about Wesley Crusher's getup from the first season. It seemed rather casual for duty wear. However, upon rewatching, I figured out that this is probably the cadet/acting Ensign uniform. The three stripes at the top represent the three divisions (as shown on the regular uniforms). A cadet probably doesn't commit to a track until later.
Worf makes a big deal about Klingon honor, even to the point of it getting explicitly mentioned in "All Good Things" as something he has but others do not, the question becomes why? The reason - because he wasn't raised by Klingons! He heard all the stories and legends of Klingons, he learned about what they were supposed to be and tried to live up to it, just as we have romanticized stories of Samurai behavior in modern day times. Actual Klingons are more pragmatic - honor is still a big thing for them but it's not as important. Worf, a stranger in a strange land, defined himself by the stereotypical Klingon ideal and as such became more Klingon than Klingon in some ways. In other words - Worf would respond to a challenge of honor specifically because of his own personal honor because that's what is important, a regular klingon would probably be more concerned about other's perception of his honor and be more willing to let small things slide.
I noticed that the Cassandra Truth trope is rarely used on this show. It's particularly noticable in "Cause and Effect", when Beverly hears voices (from a past timeline). People don't waste time talking about how it's impossible, they try to figure it out. Someone getting flatly shut down is an indication that the rejector is Not Himself. Not only is this a subtle but effective illustration of their status as True Companions, it makes sense that, given the weirdness they've already run into, they'd be very open-minded. There have been episodes where they are the Cassandra to their superiors in Starfleet.