Continuity mistake: During the Anakin/Obi-Wan fight scene Obi Wan switches lightsabers with Anakin. When Anakin is strangling him we can definitely see that Obi-Wan is holding Anakin's lightsaber in his right hand (note the hilt design), but when the shot is reversed Obi-Wan is holding his own lightsaber in that hand. (01:46:30)
Continuity mistake: When Anakin is in the medical centre lying on his back being transformed into Darth Vader, you can see the main part of the mask being lowered into place but Anakin is not wearing the neck section of the mask that it connects to. We then see the main part lowering directly downwards, in the next shot the neck section is in place. (02:01:20)
Trivia: George Lucas makes a cameo appearance during the opera scene. He is the blue faced being, named Baron Papanoida, that you see outside Palpatine's box. It marks Lucas' first and only appearance in any of the Star Wars films; also in that scene is Lucas' daughter Amanda and her boyfriend. Lucas also reportedly provides the sound of General Grievous' coughing.
Other mistake: During the scene of Anakin's transformation into Darth Vader, there is a close up shot of his face just before his helmet is put in place. All of his face is shown as being badly burned with the exception of his eyelashes, which are still impossibly there. Subjecting one's face to any heat source hot enough to sear one's face will also burn away one's eyelashes as well. (02:01:25)
Continuity mistake: When Mace Windu and Palpatine are in his office after the lightsaber battle, Palpatine scrabbles into the corner as Windu paces towards him, ending up directly over him with lightsaber pointed at his throat. As Anakin walks in, Palpatine is already backed into the corner and Windu needs a few paces to get to him. (01:09:55)
Continuity mistake: When the Emperor and Yoda flip backwards out of the pod from the "kickback" of the Force lightning the Emperor falls onto the sloped side of the pod.When they show him again he is hanging on the side of the pod with handles.(If you look at the pods each has a sloped side and a part with guardrail or handle)
Revealing mistake: When Anakin and Obi-Wan are fighting on top of the table, after Anakin kicks Obi-Wan, we see a wide shot of Obi-Wan hitting the table, followed by a close-up of Anakin charging at him. You can see that the one who comes toward him is not Hayden Christensen, but his stunt double. (01:51:15)
Continuity mistake: Just before the lightsaber battle between Mace Windu and Darth Sidious, we see the lightsaber of Sidious ejected from his sleeve and he grabs it with his finger down the length of it. We then instantly cut to a wide shot and he's suddenly gripping it with all his fingers curled in. (01:08:30)