Continuity mistake: In the scene where Anakin arrives on Mustafar and tells R2-D2 to stay with the ship, he pulls the hood of his robe over his head with two organic hands. His right hand should be mechanical. [This mistake is mentioned in the audio commentary: this shot is taken from a shot of Obi-Wan later in the film when leaving Padme's apartment. Still a mistake, though.]
Trivia: We see in the movie that General Grievous is permanently coughing when he talks. The cause of this can be found in the last episode of the animated, Emmy-winning TV series "Clone Wars." In that episode, Grievous kidnaps Palpatine and before leaving into space, he is attacked by Mace Windu, who destroys part of his armor in the chest, making him cough for the first time.