Phantom Menace
Bring in Hayden Christiansen (or a more competent young adult actor) right away, so we're not scratching our heads over the age difference between him and Padme. After Darth Maul kills Qui-Gon, have him standing over Obi-Wan as he hangs off the edge of the platform and then deliver the mysterious line, "I was ordered to kill only one of you." Then he takes off.
No Jar Jar.
Attack of the Clones
Bring in some other screenwriter for at least the scenes between Anakin and Padme. With a better writer, it could have been one of the great, tragic movie romances.
Still no Jar Jar.
Revenge of the Sith
After the attempted assasination of Padme, when they catch up to the mysterious assassin, the camera focuses on his hand as he slowly pulls out a double light saber. Dun dun dun! It's Darth Maul! After another 3-way light saber fight, Anakin is the one who kills him. How appropriate since he's taking his place later.
Still no Jar Jar.