The ways I would have made episode I better:
-no Qui-gon Jinn, sure he was okay but everything he does would be more effective if Obi-Wan did it, would give us better character development, plus we'd know he's awesome, because hey he is Ben Kenobi.
-Make Jar Jar less annoying, still comic relief but in a sniveling coward way rather than a "Izza stepped in da poopy" way he was in the first. Instead of winning by accident in the battle, he overcomes his cowardly nature to be a hero.
-Make Anakin 18-20 basically Luke from IV, that way when they say he's too old to train as a Jedi its an even bigger deal and his relationship with Padme is less weird. Also cast a really likeable and non-emo actor as him, portray him as a paragon of lawful good, that way his fall is more devasting.
-Lose the starfigther battle, it made no sense because that was the only battle that mattered, the gungans, infiltrating Naboo guards and Jedi's battle would have been for nothing had the droids not been deactivated. Make the viceroy only able to disarm them, making Padme's move important, but the other two battle are there to make sure she achieves her goal. This also leaves Anakin free to...
-Kill Darth Maul, so right now we've had Obi Wan get his arse handed to him by Maul, he's all alone and his sabers out of reach, Maul's gloating over him. Suddenly we see the saber slide along the ground with the force and into...Anakin's hand (everyone's assuming it was going to be Obi Wan at this point), who crudely cuts Maul in two.
It ends with Jar Jar having earnt his hero status, Obi Wan deciding to go against the wishes of the council and train Anakin and some early ground work in the relationship with Padme, like a stolen kiss or something.
For II and III:
-Have someone else like Morgan Freeman as Mace Windu, Samuel L Jackson works best with characters full of emotion, which is why he should play Jango Fett, imagine him screaming at "Bantha fodda" eating Jedi as he fires both pistols, simply awesome. Also that would mean a clone army of Samuel L Jackson which is also awesome.
-Have the reason Anakin goes evil be due to Palpatine manipulating him to think the Jedi are corrupt, that the Sith are the real good guys. Stuff starts escalating, he keeps trying to do what he thinks is the right thing, eventually he hits the point of no return and becomes the Vader we all know, hating himself for doing so.
P.S. I am by no means a starwars fanboy, I've only seen the original trilogy a handful of times, the new trilogy only once, never read any of the EU or that stuff. I was just having this discussion yesterday with a mate.