Lightsaber battles. Really outstanding choreography, especially in the final Obi-Wan vs. Anakin bout.
Visual effects. I know this gets said every time there is a new blockbuster, and it will probably be said again, but I think this was truly the first time that there were such extensive visual effects but I never noticed them as effects. The digital people look like real people. The opening battle sequence was incredibly intense. Gorgeous, even.
Loose ends. Pretty much all questions were answered and everything ties together nicely with the original trilogy. Even the set style segues into Episode IV.
Ewan McGregor. He was compelling as Obi-Wan, and perhaps the one actor most responsible for making the story work. His reactions during and after Anakin's transition to the Dark Side were powerful.
Dialogue. It was horrible. Beyond bad. B-movie campy. I don't think that the opening-midnight true-fan audience was supposed to snicker at the melodramatic Anakin/Padme scenes, but they sure did. His turning-to-the-Dark-Side scenes, too. Pretty much every time Anakin had something to say, you could expect the worst. The others didn't fare much better. I like Samuel L. Jackson and Natalie Portman, but when they're working with so little, it's hard to. Why, oh why, couldn't Lucas farm the script out to somebody, or at least let someone else punch it up a little?
Some of these I'm sure I just didn't catch, but . . .
What exactly is the connection between the clone army and the stormtroopers? They didn't all talk like Jango Fett in later movies, implying that they aren't the same group. If the stormtroopers aren't clones, why not? And what happened to all of the clones? Are some stormtroopers clones and others new recruits? Or is there just no connection at all, despite the heavy symbolism of the similar costumes?
What was Yoda talking about regarding Qui-Gon? I know that it was probably supposed to explain why he didn't disappear when killed as later Jedi do, but it didn't make sense to me. Qui-Gon learned how to survive death and come back as a ghost. He didn't disappear when he died, so the technique either doesn't make you disappear (which doesn't explain why later Jedi disappeared, defeating the purpose of mentioning it) or it's something the still-conscious "soul" does after death to come back (which also doesn't explain why later Jedi disappeared, again defeating the purpose of mentioning it). The second possibility also seems to not fit with the whole idea of the Force as a kind of Buddhist all-as-one super-entity. The only thing I can figure is that Qui-Gon learned how to come back after he died, and now he can teach Obi-Wan how to do it "automatically" by disappearing . . . but Yoda didn't say that. At least I don't think he did.
Why did they think a good place to hide Anakin's son would be on his own home planet and with his (step-)relatives? And keep his last name Skywalker? Yeah, that's not suspicious . . . I guess that's really a question raised by the other movies, but the events actually happened in this one. It seems like "with his family" is the last place Luke should go.