These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
In the west, Noike is almost universally derided for her spotlight stealingrole in OVA 3. In Japan, opinion of her is a lot more balanced, and is overall accepted and liked by the masses. This is probably due to Kajishima's continued releases of doujinshi and novels that expand upon the 'verse. Americans were pretty surprised by Noike due to No Export for You.
Ayeka is a lot less liked in the west than she is in Japan.
Base Breaker: Ayeka, Mihoshi and Ryoko fit in this tropes. Is Ayeka a sweet princess who cares about the others but doesn't really now how to express it properly, or a bitch who only cares for herself? Is Ryoko a Jerk with a Heart of Gold who did funny antics or an annoying Jerk Ass who constantly abuses others and did horrendous acts? Is Mihoshi a sympathetic Cloud Cuckoo Lander or an irritating stupid character who always gets her friends in trouble? In Mihoshi case, it should be note some people likes her Genius Ditz OVA version and only dislike her TV version where she is more dumb.
Complete Monster: Mad Scientist Kagato is an intergalactic researcher who utterly lacks anything resembling conscience. Kagato turned on his mentor, Washu Hakubi, and imprisoned her for thousands of years, hijacking everything she had left behind, including Washu's created 'daughter' Ryoko. Brainwashing Ryoko, Kagato sent her to discover the truth of the 'greatest treasure in the universe,' having her hunt down traces of it...and then destroy the worlds that contained it to make certain nobody else could replicate his discoveries, whether they were inhabited or not. Over 3,000 worlds met their fate this way. After losing Ryoko, Kagato continued the process himself until he discovered her alive on earth. He wastes little time in trying to kill Tenchi and his Unwanted Harem and succeeds in blowing Tenchi apart from his ship. When Ryoko offers her life in place of Tenchi's, Kagato merely responds he'll just kill both of them. When Wahsu is freed, Kagato decides to 'reminisce' about the old days by drawing on his ship's power to destroy the earth. Kagato is defined by his drive for his 'scientific method.' Anything that gets caught in his path is simply collateral damage to that end, no matter what.
Die for Our Ship: Ryoko vs. Ayeka, though it is implied that Ryoko wins in the Tenchi Universe continuity. There is also Sakuya in Tenchi in Tokyo, and the Ryoko and Ayeka fandom rioted over this (until Sakuya died).
Also many of Ryoko's actions in Universe. From mocking Ayeka and almost making her believe that Tenchi loves her the most when Ayeka is genuinely distressed upon having to leave to Earth with Sasami and never return, to... well, see Moral Event Horizon.
Mihoshi in the original series before her inevitable Flanderization later on.
Also Kagato from the Universe version to those who found him an even more intimidating villain than the original.
People forget that Kiyone became very popular after her first appearance during the Mihoshi special of the OVA series. Back then, she wasn't meant to be a main character, but was made one in Tenchi:Universe and beyond.
Ryoko initially counted for this before she fell for Tenchi.
Fan-Preferred Couple: Among western audiences, the majority of fans seem to feel that Tenchi should choose Ryoko. The number of fan fics where Tenchi ends up with Ryoko hugely outnumber the ones where he picks Ayeka or one of the other girls.
Foe Yay: Ayeka and Ryoko's fighting over Tenchi across all continuities is so intense and involved that at times it seems like they care more about each other then about Tenchi. Tenchi Universe sort of acknowledged this, with an alternate universe where Pretty Sammy shoots Ryoko and Ayeka with a beam and makes them fall in love with each other.
Genre Turning Point: Although Urusei Yatsura is generally credited as the first harem show, Tenchi really set the genre on fire, launching a host of imitators. Perhaps its biggest innovation was to make the male lead a soft-spoken, incredibly nice guy (and have this be why the girls all like him) as opposed to UY's Ataru, who is a sex-crazed jerkass. It was easier for viewers to see themselves in someone like Tenchi, which amped up the wish fulfillment.
Magnificent Bastard: Kagato. In the OAV he's a stylish, Faux Affably EvilWicked CulturedBad Ass. In the Universe series, he sets up Ayeka as a treacherous usurper to the throne, causing the whole group to travel all the way to Jurai just to have a fight with Katsuhiko /Yosho by using Yosho's name as a way to get political power in order to force Yosho into action. He may have achieved this goal, by dying in a fight with Tenchi, Yosho's grandson.
Misaimed Fandom: Both Ryoko and Ayeka are supposed to be viewed as comedically psychotic bitches when they fight with each other over Tenchi or whatever else. You're not really meant to root for either of them. The idea that there are fans who view one as in the right while the other is in the wrong is strange.
Ryoko, even though she gets on a lot of people's bad sides,.. a few things she's done are actually despicable. In example, in the Universe series she buys food, enjoys a sun tan and gambles away the money that was supposed to be used for food for everyone including her "beloved" Tenchi, making them wait as they slowly starve to almost death. (to fix her screw up, she robs a bank, which is double bad and stupid due to how they are on the run.) She keeps refusing to listen to Ryo-Ohki trying to tell her she's pulling shit!
Also, Ryoko attempts to kill two girls merely for liking Tenchi. One of them, Mayuka, was technically Tenchi's daughter — and Ryoko attempted to drop her to her death into a lake before she changed her mind at the last second. Thank GOD she's slapped for that by Tenchi of all people.
Haruna passes this for lots of people, when you see that in her despair to consummate her love for Yosho... she brainwashed and raped Yosho's innocent grandson Tenchi.
OAV!Kagato does this via mindcontrolling Ryoko to attack the group and Tenchi, then by killing Tenchi in the upcoming battle (with only the timely intervention of Tsunami bringing him back) — while forcing a kidnapped Ryoko to watch!
Nightmare Fuel: While being a provocative series, it definitely shows a few scenes that are just frightening: Toys that have blades emerging from their bodies, the black monster Kain who seems to do almost anything including the ability to turn into a black dragon demon, an evil Jurai knight decaying rapidly into a skull-faced corpse which you have can fun with being that it was shown everytime Tenchi starts, the earth being cut in half, Hotsuma turning into a monster, the eldritch-y dream realm (not the one with shards, but a weird black and white Picasso drawing type place) of Yugi, Kagato (especially his OVA incarnation), Ryoko's bestial form, and Sakuya being absorbed into Yugi against her will....Have fun with that.
Kain. He's a writhing mass of dark energy with a sadistic personality, takes on a pure white mask with a Slasher Smile, and later turns into a monstrous dragon, demon, shark thing.... one of the first things he does when he lands on earth is rip a guy in half and throw him at a small group of teenagers. Sheesh.
Romantic Plot Tumor: Probably one of the shortest examples. Three quarters into OVA 3, an entire episode is spent exploring the budding romance between Misao and Mashisu. This might not seem like a big deal, but considering that OVA 3 is only seven episodes long and the love reveal distracted from other more pressing plot elements, this definitely fits.
Stoic Woobie: Katsuhiko/Yosho in the Universe version instead of leaving due to discrimination on his half human lineage and "women" in the OVA; he had lost his first true friend, a child eating monster who was about to change her ways, till the Jurai force came and beat the hell out of her, then calling her a freak when she revealed her true form and running away. Then in his adulthood, her's forced to kill his best friend who had become power-hungry and killing everything in site, next wanders across the galaxy out of guilt and finding a place for his lover who wasn't royalty, so that they can love each other without being social class discrimination. She up and dies before they even arrive there. When he finally has a kid, she dies from having to expel an immense Jurai Power to kill a black mass of demonic evil, she lives nine years later to have Tenchi and then dies when her son was very young, causing him and Tenchi's father, Nobuyuki to hate winter for a while, being the time she died. Then we get the present where that power-hungry friend has literally come back from hell to use his identity and frame one of his relations for treason, leading to a long chase until he finally meets him again and is understandably distraught about killing him again, to the point that he considers double suicide as a solution. After that mess, that first friend has returned to being a bratty trickster who's now Yandere for him, to the point that she creates a clone with her and his grandson's DNA and have that said clone rape and take him to her dimension till he comes over himself. And that lover I'm talking about, her ghost manipulates his grandson's memories and uses him as a substitute for her former lover. But he continues on being solemn and sometimes cheerful.
The Scrappy: Noike for American fans but the obvious is Yugi for her smugness and the Karma Houdini for the truly monstrous acts she commits.
Both Mashisu and Misao from the OVA 3 are almost universally hated because one episode focus on them romance instead the plot. And Sakuya is seen as an annoying Mary Sue for a large portion of the fandom even when she deconstructs the Mary Sue concept in the first place.
Hiwa Takahashi in the manga. She is Tenchi's childhood friend and has a crush on him. That's sound like potential for good stories, right ? Well, she was only a one-shot character and the story focus more on Ayeka and Ryoko and her relation with Tenchi is never really explored.
What Do You Mean, It's Not for Kids?: I have no idea what Toonami was thinking. They had to do a lot of censoring to be able to try passing it off as a kids show. Even when they moved it to [adult swim] they couldn't get away with showing the female characters frequently nude.
Funny truth is, most of the current US Tenchi fans are those kids from the Toonami era, having grown up after the end of the show's run, looking back one day for some reason to rediscover their fandom of this show… and then learn a few new things about it along the way. This is ironic considering that the revived 2012 Toonami premiered Tenchi Muyo GXP, and the Faithful mostly hate it.