I'm going to repeat some things that have been mentioned already, but I have some that haven't been brought up yet.
Anakin should have been a different character altogether. He should have been someone we could respect; a real hero instead of a powerful, out-of-control whiny kid. The whole "chosen one" idea should have been scrapped. Anakin should have been a normal Jedi, corrupted by a desire for power (though this would only have begun as a result of some tragedy in the middle of Episode II--his mother's death could have been part of it). If the Battle of Naboo had still happened, he shouldn't have been involved in it at all and IMO he should have been a background character in Episode I, and become gradually more prominent.
I hated the whole Padmé/Anakin romance. It seemed too forced and it shouldn't have been such a big part of Episodes II and III. If it had been kept fairly background like in the OT, then it wouldn't have been so bad.
Jar Jar. He could have been such a different character, but everything about him was goofy and retarded.
The bad guys were just for looks. If we had explored their characters a bit more, they would have been far more convincing characters.
Lightsabre fights should have had more dialogue. Fast-paced action would have been OK for me, but it should have been interspersed with the Sith taunting his Jedi opponent and trying to make him lose control. If more of the fights had been done along the lines of Anakin vs. Dooku in Episode III, it would have been far better (I think--I haven't seen Episode III for a while).
The prequels should not have been treated like a reboot of Star Wars. PT technology should have looked less advanced than OT technology. The SE should have given us more advanced displays like Adywan did so that they would be able to use slightly more advanced technology, but it should not have been more advanced than the OT's tech.
I think Lucas and ILM forgot about the fact that people loved that the Star Wars universe looked lived in in the OT. Everything in the PT looks new and clean, and if there is dirt it is CG dirt and thus looks fake. Far too much focus was on the visual effects and eye candy in the PT and thus it fell into the trap of other Sci-Fi movies that the OT had avoided (and that's another thing: the PT was too much science fiction whereas the OT was space fantasy).
The PT tried to tie everything together and by doing so effectively shrunk the Star Wars universe to a tenth of the size. C-3PO being built by Darth Vader? That's garbage. Everything also seems to revolve around Tatooine, which is supposedly an insignificant planet no one's ever heard of, way out on the edge of the galaxy. The only Star Wars movie that doesn't feature Tatooine is ESB (unless it does too...). Not only that, but everything happens in the same general area of Tatooine and we even see Jabba in TPM. Boba Fett loses a lot of his mystique and is way too involved in the main story. George apparently lost his ability to invent new characters when he wrote the PT.
The Jedi should not have been so well known. In the OT, Han has never heard of the Jedi or the Force, yet he was something like 14 when the Republic fell, Luke had never heard of the Force, Imperial officers scoffed at Darth Vader's "sad devotion to that ancient religion" yet one would think they would have heard about the kinds of feats Jedi had been capable of. Also, Jedi should not have been so powerful. In the PT they had way too few limitations.
CGI was over-used.
Dialogue was terrible.
The prequels should have been made so that that Star Wars could be watched in chronological order. Now the surprise of Darth Vader being Luke and Leia's father is ruined in Episode III, Jabba's reveal is ruined, Boba Fett and Slave I are no longer unique to Episodes V and VI, we see Jawas, Tuskens, and Sandcrawlers in Episode II, the Emperor is too prominent in the PT--his appearance should have been a shock in Episode V, etc.
The prequels spoiled a lot of continuity. Padmé should not have died in childbirth, the Force should not have had a scientific explanations, etc.