Audio problem: In the scene where Anakin turns to the dark side, Darth Sidious says, "You're fulfilling your destiny, Anakin." As he says this, his head is shown from behind and is in shadow, but the words don't match the motion of his jaw, and his profile shows that his mouth is moving after the words are heard. (01:12:20)
Continuity mistake: Just before leaving in his spacecraft to go and fight against general Grievous, Obi-Wan Kenobi is seen being briefed by Clone Commander Cody. During the briefing, you can see that at least one of the clone troopers on the right does not have the same head as the Clone Commander. But, when Obi-Wan climbs onto the wing of his spacecraft and enters it, the clone troopers on the right suddenly all have the same head as the Clone Commander.
Continuity mistake: When Anakin and Obi-Wan are on their way to find Palpatine, destroyers appears shooting at them. In the shot behind the destroyers while they are shooting we can see the door behind Anakin and Obi-Wan are closed. When it cuts to a shot of them the door has suddenly opened a foot in a second. (00:08:35)
Continuity mistake: In the beginning, when Obi-Wan and Anakin are returning after saving Palpatine, you can see their ship approaching the platform is about to go under a large shadow. But in the next shot, it takes quite a while for the shadow to even touch the ship, and the shadow is of a different position/size. (The shadow is from an over-hang above them, for other ships I assume).
Continuity mistake: In the Palpatine/Yoda lightsaber duel, during the second time they lock sabers, Palpatine's blade is pointed down, then in a closeup of his face, his blade is at an upward angle. Then when it cuts back to Yoda, his blade is pointed down again even though blades were constantly locked. This may only be noticeable in widescreen.
Continuity mistake: When Ki-Adi-Mundi is killed on Mygeeto, as the clone troopers stop and point their blasters at him, the area where they're standing consists mostly of sand. In the following shots, the sand is gone and there is only snow there (best seen in the shot from behind them). Even though it's snowing, the snow couldn't have covered up the sand that quickly. (01:18:10)