Tenchi Muyo!/WMG

Washu used some feline DNA when making Ryoko
Self-explanatory, really. What with the catlike pupils, occasionally appearing tail, habit of sleeping all day on a rafter...

Ryoko actually had control over her own body when she was with Kagato (sometimes)
Ryoko was kidnapped when she was young(ish), and her memory was wiped or she blocked them away. Kagato (at first) had to 'control' her because she was not yet at the level of proficiency he wanted. However, he liked to play with his victems, and to torture them. Unfortuneatly Ryoko could remember everything that happened when he took over he body, and eventually she was given a choice: She could either be in control, and kill the people herself, or she could let Kagato take control. Eventually she decided to take control because she knew the people would die anyway, and at least she could refuse to torture them like Kagato would, instead giving them a quick (and essentially painless) death. She is a murderess, but not because she hates people.

The cast never really made it back to their original world after the Time and Space Adventures arc in Tenchi Universe.
The world they end up in for the second half is almost the one they first came from, close enough to it that even Washu is fooled, but it's actually a new universe created based on Ryoko's promise to Tenchi while inside of Washu's machine; a world where things immediately arranged themselves so Ryoko and Tenchi got to go on a "real" adventure together. This is foreshadowed immediately before Ryoko made her promise, when she tells Tenchi not to say anything to her or they might never get home. It just turned out that she didn't need him to say a word to start wishing for another world the machine could grab onto. (Note: this entire WMG might only be true for the dub, as I've never seen the sub.)

Mihoshi is actually a brilliant Galaxy Police supercop faking idiocy.
Mihoshi uses a level of Obfuscating Stupidity the Irresponsible Captain Tylor could only dream of. Mihoshi's ditzy persona is to put both her opponents and superiors off guard.
 * By the Word of God she's a combination of a Bunny Ears Lawyer, Cloudcuckoolander and The Fool. That is, she's actually a pretty competent cop (when she manages to concentrate), but so airheaded that it takes a full load of the famous Kuramitsu Luck from making her the Butt Monkey. But somehow it even works.
 * in the OVA, Mihoshi actually used to be far more level headed, but at some point in the past she had a horrible accident in a relationship (believed to be a Chosin level character) which fractured her psyche, leaving her as she is now. the only reason she survived at all is that she is a blood relative of Washu.
 * It was a suicide attempt caused by her lover leaving her. When the family revived her, she became the person we see today

All the girls are amoral sociopaths.
All the girls in the show including Sasami and Ryo-Ohki (but with a possible exception of Mihoshi) are borderline sociopaths from an alien culture where might seriously makes right and they all behave themselves only because they're attracted to Tenchi and want to please him. Witness Ryoko's initial murderous intentions, Ayeka's self-righteous imprisonment of Tenchi and her following condescending attitudes, Sasami's near-lethal prank and Washu's apparent disregard for Kagato's threat to destroy planet Earth, as well as her little "joke" of leaving Ryoko alone bound and helpless in dark, apparently a state she has a serious phobia of. Also in the new series, see Mihoshi's brother and father who seem to be quite willing to destroy Earth over one man's imagined slight. On whole, it seems like the inbreeding is really getting to the leaders of the galaxy.
 * Kiyone is perhaps a little unstable, bi-polar, and suicidal but is not an amoral sociopath.
 * And who is the cause of Kiyone's melancholy? Mihoshi is the reason Kiyone is trapped a backwater planet, with a sidetracked career, unable to succeed at anything, and slowly losing an already fragile grasp to sanity. Just as planned. Combined with the previous genius Mihoshi theory it becomes clear that Mihoshi is intentionally driving Kiyone insane, perhaps even to turn Kiyone into as much of an amoral sociopath as the other girls.
 * Wouldn't it make her as an amoral sociopath as all the other girls, then?
 * Not yet, but a few more years with Mihoshi will make Kiyone an amoral sociopath equal (or surpassing) the other girls - All Mihoshi's manipulation.

The Ayeka/Tenchi/Ryoko love triangle is a Type 5 rather than a Type 3.
Ayeka's most common outburst when unable to find Tenchi is "Where's RYOKO?!" The more logical question would be "Where's Tenchi?", but that's only if she's looking for Tenchi. Rather, Ayeka is concerned that Ryoko is off alone with Tenchi because she wants the space pirate for herself. Her increasingly erratic and violent actions in "pursuit" of Tenchi are actually intended to sabotage any attempts at romance with Ryoko, so that Ayeka can have her all to herself. Thus, it doesn't matter if Tenchi winds up seeing Ayeka as an overbearing, violent harpy. The one she wants is exactly the same way.

Ryoko and Ayeka aren't interested in Tenchi at all but using him to help cover up their attraction to each other.
They pretend to or subconsciously fall in love with this obviously asexual guy knowing he won't return their affections to cover up their lesbian tendencies. They're more often than not more obsessed with each other than they are with Tenchi. There's also the alternate universe where Sasami hits them with a love/friendship arrow which takes down their emotional barriers and almost immediately lets them act on their desires for each other while ignoring Tenchi completely.

Lady Funaho and Lady Misaki are lesbian (or at least bisexual) lovers.
One of the more popular theories shared by many Western fans (especially among fanfic writers, who seem to delight in further developing the idea), is that Ladies Funaho and Misaki are not only the joint Empresses of Jurai and wives of it's Emperor (polygamy apparently being socially acceptable on Jurai), but that they are also lovers in their own right. It's even been suggested that their feelings for one another are more intense than those which they have for their husband. These theories may be further explored in the novels (which seem to delight in exploring not only extremely complex and entirely unexpected relationships, but also incestuous ones — EVERYONE in the novels is related to everyone else, more often than not by blood), but they are in no way encouraged in either the OAVs or the spin-off manga.
 * Similar theories have been applied to the Tenchi/Aeka/Ryoko relationship (often with one or more of the other girls thrown in for good measure). See also Everyone Is Bi.
 * They certainly couldn't be lesbians exclusively, because Yosho clearly stated that he was kicked out to the Academy (to study and find himself a suitable Love Interest -- which, incidentally, was exactly what happened: Seto's gambits rarely fail, if ever) because of his affair with Misaki of all people. And both women certainly bore Azusa's children. What's definitely true is that both their marriages are mostly of convenience (well, with Funaho it's less so), and Azusa is still hopelessly in love with his mother-in-law. Seto is suitably honored but doesn't really reciprocate (efen if Utsutsumi probably wouldn't mind).

Jurians are plant-people, like Count D and his family from Pet Shop of Horrors
This is kind of being played off the comment in the abridged series regarding the Jurians being a bunch of inbred space hippies. Which is kind of true, since they clearly managed to somehow make the 'royal lineage' thing work. This doesn't work with animal species (like humans), since the traits brought out by inbreeding animals tend to be severely detrimental to their well-being, and especially their appearance. However, plant species aren't really adversely affected by either inbreeding or cross-breeding, and neither are the Jurians. Also, most if not all of their technology is tree-based. Then again, every member of the noble family is psychotic.

Kain killed Achika and banished Tenchi to the OVA dimension with the Ditzy Kiyone as his mother
Kain recognized that Tenchi's the biggest threat in his attempt to kill Achika, so he banished him so he won't interfere through some reincarnation to the OVA universe where we first meet him. However, Tenchi has some memories of his real mom and applied them to Kiyone mistakenly.

There is a serious male/female gender imbalance in Jurain Empire and the galaxy as well
Alternately, there are enough males to go around, but they tend to be sterile. This would explain why girls would fall for people like Tenchi and Seina, and be willing to put up with a polygamous relationship.
 * From the looks alone that's not probably the case.

Normal Earth humans with a core unit have power comparable to a Jurian battleship

 * In Dual! D states that light-hawk wings can be generated by normal humans in Dual via the core units, and that the males of "this planet" can generate especially powerful ones. Which goes against most of the other information concerning the disparity in power between humans and other galactic citizens.
 * Of course given that Kazuki has the same name as Tenchi's great-grandfather, who knows if that "Earth", is somehow the source of Jurai?
 * There isn't really any disparity -- IIRC, people of the Galaxy are simply augmented in various ways, and Earthlings in general are not. Remember GXP: Seina had quite a hard time keeping with other cadets, until they've realized that he's unaugmented. Then he got the treatment and voila! -- no disparity to think of.

The OVA universe and the TV show universes are all canon to each other through Parallel Trouble Adventure Dual
Dual, from the creators of Tenchi Muyo, tells the story of two parallel universes. One of these universes happens to be the Tenchi Universe continuity, while the other is the Tenchi In Tokyo continuity. And what happens when Kazuki and Mitsuki merge the two universes together at the end of the show? They create the OVA timeline!
 * That's exactly what Word of God states to be. Some details (even major) are really off (for example, the key continuity is Ryo-Oh-Ki, not Dual, thought this one is important, sure), but all Kajishima's works (and some not his, like most Tenchi spinoffs) are alternate continuities of one big Multiverse.
 * Word of God never said that. Kajishima stated that he never even watched Tenchi Universe or Tenchi in Tokyo, let alone considered them part of his multiverse.

Kazuki Yotsuga, from Dual Parallel Trouble Adventure, is the father of the current emperor of Jurai, and Tenchi's Great-Great Grandfather
Kazuki and his harem end up going into space with Zinv after the end of episode 14 in Dual. At some point in their journey, a space-time phenomenon ends up flinging Kazuki and Zinv thousands of years into the past. Zinv ends up buried on planet that Seina found it on in GXP, and Kazuki ends up stuck on Jurai, where, with no way to get back home, he eventually settles down and marries, eventually becoming the father of Emperor Azusa Jurai, Great Grandfather of Tenchi.
 * Possible, but not really substantiated. Azusa's father is indeed called Yotsuga Kazuki, and he's an outsider married into the family, but the circumstances of him doing so (explained in one of the novels, "Azusa", IIRC) are really incompatible with him being that Yotsuga Kazuki. It's more probable that Yotsuga the Tenchi's great-great-grandfather is the Dual!'s Yotsuga Identical Grandson.
 * Identical Grandson from D judging by Seikishi revelations.
 * Artificial human through his mother's side, apparantly.

One or more of the characters is a Time Lord.

 * It's much, much worse in reality. After all, Time Lords are just Sufficiently Advanced Aliens, while Choushin are Physical Gods, and Tenchi himself is.
 * At this point, its most probable that one of Those Two Guys from Tenchi's school is the Time Lord, and the other one is the companion. They'd stand out more if being a Time Lord wasn't practically mundane for the Masaki household.

Sasami is Haruhi Suzumiya.
Witness how Sasamie uses romance manga as a guide to help Ayeka and Ryoko to gain Tenchi's affections -- like Haruhi, she is a great believer in tropes. Observe how all the characters from the Tenchi verse reappear for Magical Girl Pretty Sammy, a Magical Girl series in which Sasami is the heroine. The only reasonable explanation is that Sasami is Haruhi Suzumiya who made a universe in which she would get to play with an Unwanted Harem; however, she got bored of this and reformatted reality to make herself a Magical Girl. Some time later, she reformatted it again into the series we all know and love...
 * It follows, then, that Tenchi, established as the avatar of a god more powerful than any of the known ones, is Kyon.

Tsunami is Haruhi, or at least an aspect of her
When Haruhi finds out about her powers, she restructures the universe into the Tenchiverse, deciding to focus on espers and aliens over time travelers and sliders (disappointed with Mikuru?). She also restructures herself into the Choushin, Tsunami, Washu, and Tokimi, because, hey, Three Faces of Eve is a trope, and it means she'll have someone to talk to. After having her fun and rendering the universe unrecognizable and traveling back to before her birth, she/they decide to try to find Kyon again, because things were fun when he was around. She, being in control, now knows that Kyon was a god even higher than her, and, having restructured everything so much, only remembers that about him, nothing else, thus setting the plot of Tenchi Muyo- the Choushin searching for "a power greater than themselves", aka Kyon, now known thanks to several universal reboots as Tenchi. The thing with fusing one aspect with a young girl, Sasami, was an attempt by the nice part of her, Tsunami (also motherly instincts) to create a vague semblance of what was before. The genki part and most of the creativity went into Washu, and the bitchy part went into Tokimi.

Tenchi is Shinji Ikari, and it's All Just a Dream
What, we need an Evangelion, a Haruhi, and a Doctor Who theories in here, okay?
 * Okay, and a Bleach one. Yeah, always a Bleach one.
 * Okay... Tenchi is a Shinigami, and Ryoko is a Vasto Lorde. It this good enough to you?
 * And... Washu is a Time Lord. Actually, I like that one. Washu is totally a Time Lord.
 * I've seen fics where Washu used to be married to The Doctor.
 * As evidenced below, we don't miss a 40K one any more.

Tenchi is the Immortal God-Emperor of Mankind
Well, he's immortal, he's The Emperor (in the future), and he's God... Some official arts doesn't help even a bit...
 * He ascended to the throne when he became emperor of the Jurai empire. He must have changed the capital to Earth at some point early in his reign.
 * Given the characters he surrounds himself with... does this mean that Washu is (or secretly in charge of the Techpriests?
 * No, it doesn't fit her characterization very well. She probably was back in the day, but got sealed up again around the time God Emperor Tenchi went comatose, and her followers went just as misdirected without her guidance as the God-Emperor's did. Likewise, the Sisters of Battle were once under Ayeka and Ryoko, Mihoshi was in charge of the Imperial Guard, and I would fit Tsunami/Sasami in there but the concept of such a Yamato Nadeshiko in the same universe as Grimdark would cause a matter/antimatter reaction.

The Light Hawk Wings are related to the White Light of Creation
In the Green Lantern story arc, Blackest Night, it's revealed that the combination of the seven Lantern Corps will create the White Light of Creation. Given that the Light Hawk Wings are able to create objects out of energy and other powers suspiciously similar to the Lantern rings, this White Light of Creation is likely the same as the Light Hawk Wings. Of course, this could mean that Dawn Granger a.k.a. Dove is somehow related to Tenchi given that she has an explicit connection to this White Light.

Washu is a Madgirl
And not just any madgirl - the ultimate madgirl. She is the goddess of mad scientists, from whom all others derive their inspirations from. She is the original source of all brilliance and madness. She is the Divine Spark.