Well ... it has to be the SW prequels as ever ...
Reduce meeting Anakin as a child to a short 30 minute intro then move forward allowing the Clone Wars to actually feature in the second movie.
Retain Maul as a consistent enemy until the 3rd film ...
Give the Jedis more .... life! .... more humanity. They were too cold and very difficult to like.
I could go on for hours ....................... you get the idea.
1) I would have made Jar Jar a minor character. He brings Obi-Wan and Qui-Gon to see the Gungun King and then part ways.
2) I agree with you on shortening the meeting with Anakin. I'd also eliminate the pod race entirely. It had no purpose except to sell the video game based on that scene (which was available in stores before the movie even hit theatres).
3) Make Darth Maul a meatier villain. Give him more to do. Have him torture information out of jawas and have him cow a tribe of sandpeople into submission while searching for Queen Amidala and the jedi. I'd still have him die in the end, but at least he'd be a better villain.
4) Have Obi-Wan agree with Qui-Gon that Anakin is the Chosen One, rather than train him because he promised Qui-Gon as he was dying.
5) Deffinately get the jedi to lighten up... they're not Vulcans for God sake.
6) Have some more scenes where Anakin loses his temper, make it more obvious that he's on a path to The Dark Side.
7) Have more scenes showing the depth of Anakin's friendship with Obi-Wan. That would make his betrayal more painful.
8) Have Anakin or Owen or someone mention when they tell Anakin of his mother's abduction how unusual it is for sandpeople to take prisoners. They usually just kill you, take what they want, then leave (it's my belief that Darth Sidius orchestrated the abduction and torture of Shmi Skywalker).
9) Have more scenes with wookiees. Maybe a wookiee jedi on the counsil.
10) Don't have Vader raising his fists in the air and screaming "NOOOOOOOOOOO!" when he learns of Padme's death. It's such a cliche it's a Hollywood joke.