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.
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.
Continuity mistake: When the Emperor says "I have waited a long time for this moment my little green friend." Yoda can be seen laying beside his cane on the purple carpet. When they show him standing up, he and the cane are now further back toward the wall on the tan part of the carpet.
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.
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.
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)
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.
Continuity mistake: When Obi-wan gets on the intercom with R2 the first time on Grievous' ship, as it cuts to R2 backing up against the corner hiding from the droids we can see that there is no light casting his shadow. When it cuts to R2 again two shots later, bright light suddenly appears, casting his shadow.