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.
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 Guerre stellari (1977), where a stormtrooper accidentally bangs his head on a door.
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.
The Senate votes to give the Supreme Chancellor sweeping emergency powers to go to war against the Separatist forces. This is the same ploy Adolf Hitler used to gain similar dictatorial power in mid 1930s Germany.
Like Ewan McGregor did in Star Wars: Episodio I - La minaccia fantasma (1999), Hayden Christensen made "light-saber noises" the first time he was handed one in rehearsal. After chuckling at the young star's antics, George Lucas informed him that they probably had people in Sound Effects who could do a better job in post-production.
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.