First and foremost, editting. Just because you've got a great idea for a scene, or because you shot some footage, doesn't mean you should use it. The biggest problem here is the Anakin/Amidala love story stuff. We don't care. They're in love, she's going to have Luke and Leia- we know this. Long mournful glances don't make Anakin's fall to the darkside more tragic- just annoying. We came to watch swashbuckling adventure, not pointlessly angsty love scenes with trite, stilted dialogue delivered woodenly. Hayden Christensen is a piece of cardboard with a sixpack. But there's also needlessly long battle scenes too. The General Grievous plotline was peripheral at best, but made up a large part of the movie.
Second, if there's one thing I'll always hate about this trilogy, is that Lucas is trying desperately to make me take Star Wars seriously. We're talking about a series with space stations the size of moons capable of eradicating planets, only to be foiled by a well placed vent. There's a reason we make jokes about villans attending the Storm Trooper academy. This is not serious drama. This is Sinbad the Sailor and Jason and the Argonauts with a bigger effects budget.
Third, that was not James Earl Jones, and I'll hate Lucas forever for that horrible rendition of Vader's voice.
Fourth, in the second movie, they make a big deal of Boba Fett watching the Jedi kill his father, and swearing revenge. In Star Wars canon, we know that Boba Fett killed a large number of Jedi. But not in this movie. In fact, this went against a great deal of canon, from the fighters, to details like that. Why the big deal with Boba Fett in the second movie if we don't see him in the third? (Was that a spoiler? I don't think so.)
Fifth- folks Star Wars is not, nor will it ever be science fiction. Spaceships do not science fiction make. See, there needs to be some science. This is not a gripe with the movie, but with the fandom. Star Wars is, at its core, a swords and sorcery adventure. Deal with it.
Despite these complaints, the movie was enjoyable. It was worth it, even if you're not a fan. It's a massive improvement over the last two, though it does not make up for them. Then again, could anything make up for "Meesa Jar-Jar Binks", aside from seppuku? Not really, no.