Character mistake: During the opening space battle, Obi-Wan's ship falls under attack by buzz-droids, who proceed to cut into his fighter, disabling a number of systems and leading Anakin to try some decidedly dangerous moves to get rid of them. Both Anakin and Obi-Wan are acknowledged experts in the use of the Force and both have been shown to use the Force routinely, even for relatively mundane activities. It's also been firmly established that the Force works on droids and that the Force-user can still affect others through windows, viewscreens and so forth. Yet neither thinks to use the Force to deal with the buzz-droids. (00:05:10)
Suggested correction: There's no evidence this is a mistake. In fact, it's logically self-defeating. As you noted, both Anakin and Obi-Wan are trained Jedi Knights. If the option of knocking the droids off with the Force was indeed feasible, presumably they would have done it. There are any number of reasons why they didn't (they couldn't concentrate enough in the middle of a pitched naval battle to commit a Force attack, the droids could have been attached magnetically, etc.) but the bottom line is that if telekinesis was an option they would have done it.
Audio problem: After the buzz droids land on Obi-Wan's starfighter, Obi-Wan says, "I'm hit. Anakin?" As he says, "Anakin?" his head is turned to the side, but you can see that the last word doesn't quite fit his lips or the motion of his jaw. (00:05:10)
Continuity mistake: When the buzz droid climbs on Anakin's shuttle it stands in front of R2-D2 with a rotating arm with claws. At first the arm is rotating with the claws out. When it cuts from behind the droid you can see the claws are clenched. (00:06:25)
Continuity mistake: When R2-D2 shows the hologram of Palpatine's whereabout in the spaceship, we can see R2-D2 is looking to the right. When it cuts to a wideshot he is looking to the left. (00:07:45)
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: 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. (00:09:10)
Audio problem: When Obi-Wan speaks on R2-D2's radio, the sound editor cut a lot of frequencies, bass and middle, to make it sound like a radio. But when R2-D2 puts the radio in his shell, "magically" there is a lot of low middle in the voice. It does sound like Obi-Wan is talking from inside R2-D2, if it wasn't a radio, but in this case it is and shouldn't sound much at all, when the shell cuts the high frequencies. No low frequencies + No high frequencies = No frequencies. (00:09:40)
Continuity mistake: When Anakin is on top of the elevator before jumping back inside of it, the glove is missing from his mechanical arm. After he jumps inside, he is wearing it again. (00:10:30)
Continuity mistake: As Anakin is reentering the elevator from the top, you can see the hole being very close to the entrance door of the elevator. As we see from the subsequent shot, Anakin is landing between Obi-Wan and the aft elevator wall (Obi-Wan does a half turn to face Anakin), whereas according to the hole, Anakin should have landed either directly on top of Obi-Wan or between Obi-Wan and the elevator door. (00:10:30)
Continuity mistake: When Anakin and Obi-Wan come to rescue Palpatine we see in the wideshot a battle ship in the window behind Palpatine. When it cuts to a closeup of Palpatine the ship is gone. (00:11:05)
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 Count Dooku ignites his lightsaber, his arms are up and the saber is pointing right. In the next shot, his arms are down and the saber is pointing left. (00:11:55)
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 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 goes to pick up Obi-Wan after the fight with Count Dooku, the floor is completely different from the floor seen when Obi-Wan was lying unconscious earlier in the scene - the pattern and the colours are different. (00:12:45 - 00:14:35)
Continuity mistake: When Count Dooku drops the platform on the unconscious Obi-Wan, Obi-Wan is not lying on the same part of the floor as in the previous shot of him, seen, for example, from the pattern on the floor. Later, when Anakin walks over to him, his position is different again, and the platform has moved as well. He is also lying under a different part of the platform. (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 Obi-Wan and Anakin are fighting Dooku, Dooku throws Kenobi away. Before he is thrown, his light saber is in his right hand. When we see the shot of him on the ground, it is in his left. It is back in his right hand when he gets up. (00:12:50)
Continuity mistake: When Anakin and Count Dooku are duelling, as Dooku says, "I sense great fear in you, Skywalker", Anakin's lightsaber is slanted upwards, but in the previous shot, it was slanted downwards. (00:13:00)
Continuity mistake: When Anakin cuts off Count Dooku's head we see him putting his arms down. When it cuts to Dooku falling Anakin is standing with both arms stretched out. (00:13:50)
