Continuity mistake: When Padmé is in her apartment and Anakin is in the Jedi Council chamber, they look out across the city toward each other. The position of the setting sun and the direction of its light across their locations is not consistent given what we are shown about their relative positions and the directions they are facing. (01:07:10)
Continuity mistake: When the clone troopers kill Aayla Secura, the blue-skinned Jedi, their blasters are held differently between the second and third shot. (01:18:35)
Continuity mistake: When Obi-Wan jumps to the high ground during the duel with Anakin, in the shot where he lands, his lightsaber is held parallel to the ground. In the next shot, it is pointing downwards, and in the following shot, it is pointing slightly upwards, and his left arm is positioned differently from the previous shot. (01:54:25)
Other mistake: In the final stages of the Obi-Wan/Anakin battle, they are fighting while floating over lava on a piece of metal. Just before Obi-Wan jumps to the high ground, we get a close-up shot of Obi-Wan (lightsaber pointing left off-screen) and then Anakin, (lightsaber pointing right off-screen) In this shot, Anakin's right hand is uncovered/real, and his left is gloved/mechanical, when it should be the opposite.
Continuity mistake: In the scene following the crash landing of Grievous's flagship where the shuttle is approaching the Senate's "parking garage" (not the Senate building itself or the Jedi Temple as others have said), the shuttle is approaching a section of the landing platform that is void of any other ships. However, in the following shot, another shuttle with different coloring and larger size is in plain view. (00:23:45)
Continuity mistake: During the Anakin vs Obi-Wan fight, there is one bit where they are balancing on a thin pole. The shot starts off above them and you can see that there is nothing underneath them. They take a few steps backwards while fighting, but then they both jump off on to one of the arms of the structure they are fighting on.
Continuity mistake: When Dooku uses the Force to throw Obi-Wan through the air, in the shot where Obi-Wan hits the ground and is knocked unconscious, he's not holding his lightsaber, nor does it land anywhere near him. When Anakin walks over to him later, it is suddenly lying next to him. (00:12:40 - 00:14:30)
Continuity mistake: When Owen and Beru are standing next to each other at the end of the movie, in the shot facing them, they are standing closer together than in the previous shot. (02:08:05)
Audio problem: In the beginning of the scene in the Opera House, the audience is cheering and clapping, but in the two shots where the audience is shown, all of them are sitting still with their hands in their lap. (00:41:20)