Continuity mistake: On Utapau, when Obi-Wan faces off with Grievous, Grievous sends 4 MagnaGuards against Obi-Wan. Obi-Wan Force-pulls something from the ceiling to crush the droids. But in the ensuing fight between Obi-Wan and Grievous, the ceiling thing and crushed droids are gone.
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.] (01:32:55)
Continuity mistake: When Obi-Wan meets Anakin on the landing bay of the volcanic planet, Obi-Wan comes down the ramp from the ship and removes his cloak. It lays across the end of the ramp. The shot changes, then comes back, and the cloak is now bunched off to one side. (01:42:30)
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)
Continuity mistake: In the observatory on Grievous' ship, when Anakin and Obi-Wan ready themselves to fight Dooku, they drop their cloaks on the floor in front of Palpatine, and the cloaks' positions change in the following shots. (00:11:45)
Continuity mistake: When Palpatine fights the four Jedi Masters, his lightsaber hilt changes from his to Anakin's and back again. This happens throughout the scene. [This mistake is pointed out in the text commentary.]
Continuity mistake: In the scene where Anakin returns to Padme's apartment after the fight at the Jedi temple, watch R2-D2 in his compartment in Anakin's ship as the camera angle changes. In some shots, R2's "legs" are flush with the hull of the ship, and in others, they are well above it.
Continuity mistake: When Palpatine is talking to Anakin in his office, there is a table at the end of the hall with a large object in the middle, and a gold cup on each side. When they leave the office and are talking in the hall, and a thin purple lamp/object appears on the end of it for a few shots, and vanishes whenever seen from then on.
Continuity mistake: When Count Dooku drops the platform on Obi-Wan, you can see a piece of metal fall to the ground to the right on the screen. After the duel, when Anakin goes to grab Obi-Wan, the piece of metal is gone. (00:12:45 - 00:14:30)
Continuity mistake: When Anakin kicks Dooku over the fence, Anakin stands a feet away from the fence. When it cuts Anakin has moved further away. (00:12:50)
Continuity mistake: When the Emperor says "I have waited a long time for this moment, my little green friend," Yoda can be seen lying 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. (01:45:10)
Continuity mistake: When Tarfful uncovers the escape pod for Yoda he throws the bushes to the ground next to the pod. When Yoda enters the top the bushes are gone. (01:22:20)
Continuity mistake: When Anakin is watching Padmé while she's brushing her hair, in the shot from behind him, his shadow on the wall differs from shadow seen in the rest of the scene. (00:28:15)
Continuity mistake: When Anakin is choking Padme and lets her go, she falls to the ground. She lands a few feet away from the line on the floor. Two shots later she is lying on the line. She is unconscious so she couldn't have moved. (01:42:10)
Continuity mistake: When Mace Windu and Palpatine fight, Windu backs Palpatine into the corner of the window. Note how close Windu is to Palpatine the whole time. Then from Anakin's perspective, Windu takes a few steps toward Palpatine, his saber pointed at Palpatine. When we saw it from the earlier perspective Windu never took those three steps toward a stationary Palpatine. (01:12:50)
Continuity mistake: After Anakin has told Windu that Palpatine is the Sith Lord, Windu gets on his ship which takes off. We see the ship's shadow moving on the ground right next to Anakin. When it cuts the shadow from the ship is gone. When it cuts again to a wider shot we see the ship's shadow suddenly appear again. (01:06:05)
Continuity mistake: When Anakin has just had the bad dream, Padme comes out wearing the nightdress with rows of beads around her arms. In one shot, the beads on her right arm are twisted, in the next, they're straight again. (00:30:20)
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: In the scene where Plo Koon gets blasted by his Clone Troopers, the exterior shots show he is in an Episode II starfighter (closed/pointed bow, no small rear window on cockpit canopy- best seen as the Emperor gives the order), yet the interior shots of his cockpit show he is inside an Episode III starfighter (forked bow, small rear window on canopy- same as Obi-Wan's starfighter). (01:22:10)
Chosen answer: Powerful force users seem to have some degree of control over their bodies even after death. In the later series, Luke's wife Mara Jade Skywalker only allows her body to disappear when her killer, and nephew Jacen Solo arrives at her funeral as a clue. Thus it appears that a powerful force user can simply choose if they wish their body to disappear.
Darius Angel