As one of the less popular Tenchi series, I felt like I should try and even out the opinions a little.
STORY - I'll admit it. The first time I saw this series, I hated it too. But I rewatched the whole thing more recently and found that it actually wasn't as bad as I remembered. Like the Tenchi Forever movie, I think most fans were indignant at the introduction of a "Mary Sue" character and consequently abhorred the entire series. But while yes, Sakuya was more or less an "intruder" character to our good ol' harem, she forces a very interesting situation onto the rest of the girls. After two whole other series of being fought over by the crazy women he lives with, Tenchi finally moves out and finds someone on his own. Come on now, isn't that an intriguing twist to the premise of the Tenchi saga?
It isn't even as if Ryoko, Ayeka, and the rest disappear altogether and are unimportant; rather the opposite is true. With a puppeteer orchestrating everything in the background, it gradually warps into a grand epic as they once again find themselves needing to save the world, not to mention Tenchi. I, for one, found it incredibly interesting to watch see the girls struggle with life without Tenchi, especially as they were faced with jealousy, spite, and general unhappiness at their "replacement" by Sakuya. And in the end, as everything twisted into a crazy supernatural plot... well, with so much emotional drama going on, I suppose we needed something to remind us about that other kickass blowing-stuff-up part of Tenchi.
CHARACTER - Honestly, I think the characters' depths are explored much more in Tenchi in Tokyo than in any other Tenchi, and this completely due to the fact that Sakuya exists. For once, you're able to see Tenchi as more than just an awkward shrine boy who doesn't know what to do about anything -- he becomes more human as he's allowed to interact with people that aren't aliens or freaks of science, and that makes him a much more convincing and three-dimensional character. Because of his feelings for Sakuya, his feelings for the others, especially Ryoko and Ayeka, become more clear and he's finally able to put things in a more concrete perspective. It's actually very refreshing to see him come so far when he originally wasn't very interesting at all.
Ryoko and Ayeka, as the ones most affected by the loss of Tenchi, both show fantastic character development throughout the course of the series. Their feelings, the anger, jealousy, and hurt, are very real and easy to sympathize with, and their subsequent actions expose the many flaws in their personalities which further their complexities as characters. Of course, this forces their overall characters to be a bit different from their previous incarnations, but I don't find it to be an unwelcomed change. The rest of the girls aren't as affected and consequently don't seem to stray much from the typical character molds cast for them originally.
Now, Sakuya... Sakuya is an interesting character if only because of the fact that she isn't really real. Her validity of her personality and feelings are really up to debate though, especially since she does declare herself to be real and not a puppet. In the end, I'm not really happy with the character Yugi is revealed to be; it seemed like a cheap way out of something that had built itself up to be so epic, but I guess everything can't be perfect.
ARTWORK & ANIMATION - I believe one of the other big complaints about Tenchi in Tokyo was that its art style was vastly different from the previous two series. It does take some getting used to, but I don't really think it's that intolerable in the end. The style is rounder and more feathered along the edges, so some people claim it to be a "lazier" style. It makes for some strangely stylized portrayals, but it isn't as if any of the characters are twisted out of all possible forms of recognition. And it's definitely not awful by any means.
MUSIC - A little lacking in this department, the music isn't nearly as good as it had been in previous series. It's mostly generic sounding, which means the background music always suits its scenes, but nothing really stands out. The OP/ED are quite awesome though, considering that both "Yume wa doko e itta?" and "Yamerarenai Yamerarenai" are sung by the voice actors, which is always fun.
VOICE ACTING - I've seen this both dubbed and subbed. I've always considered the Tenchi series to be one of the better early dubs, back in the days of Toonami. Ryoko and Ayeka especially had voices that suited their characters very well (though for Ryoko, I'll always be partial to her Japanese voice because it's Ai Orikasa). Tenchi's English voice I was never really fond of, but it still suited his character well enough. And the rest of the cast is very much the same in that respect.
OVERALL - Tenchi in Tokyo really deserves more credit. It threw a wrench in the great harem premise and allowed for some fantastic emotional drama. The supernatural side got a little predictable from time to time, but I don't really feel like that was the most important part of the series. It was great watching Ryoko and Ayeka beat themselves around the head trying to deal with the loss of Tenchi to another girl, and if you're a great, big, sadistic fan of character ANGST like me, then I think you'd like this series. :3