The entire "aggressive negotiations" conversation during the dinner scene between Anakin and Padmé was ad-libbed by Hayden Christensen and Natalie Portman at George Lucas' request, due to his not being happy with the romantic dialogue he wrote for that scene.
Because he wanted to be able to identify himself during the colosseum scene, Samuel L. Jackson (Mace Windu) specifically asked George Lucas if he could have a purple light-saber. Lucas replied that Jedi light-sabers were only blue or green, to which Jackson said "Yeah, but I want a purple one." Lucas said he'd consider the request. Jackson says he didn't know how it would turn out until he went in for re-shoots, which is when Lucas showed him the scene containing his purple light-saber.
When Jango Fett gets into his ship after his fight with Obi-Wan, he bangs his head on the partially open door. This was intentional, and is a reference to a famous goof from Star Wars: Episode IV - A New Hope (1977), where a stormtrooper accidentally bangs his head on a door.
Hayden Christensen claimed to have greatly enjoyed filming the bar scene, because it was all a real set, and not just a greenscreen.
Due to much of the animosity aimed towards Jar Jar Binks in Star Wars: Episode I - The Phantom Menace (1999), the working title of this movie was "Jar Jar's Big Adventure".
Anthony Daniels: As a human customer in the bar, when Anakin and Obi-Wan hunt Senator Amidala's attempted assassin, visible just after Obi-Wan draws his light-saber.
Ahmed Best: He is seen as a human customer in the bar, into which Anakin and Obi-Wan follow the assassin.