Continuity mistake: When Yoda is done with the holographic meeting with the rest of the Jedi Council about sending Obi-wan after Grievous, he gets up and walks to the trooper behind him. We also see Chewbacca follow him, stop, and cross his arms. When it cuts to the trooper saying, "The droids have started up their main power generators," we see Chewbacca still walking and stopping, but this time he doesn't cross his arms, he places them on his hips. (00:47:20)
Character mistake: In the scene where Mace Windu and the other three Jedi attempt to arrest Palpatine, the first Jedi that Palpatine kills practically has his back turned to him, which is not something a Jedi Knight who is trained to be mindful of his surroundings would do. As we can see in the film, it takes Palpatine several seconds to stand up from his chair, draw out his lightsaber, threaten the Jedi, leap over his desk, and then lunge at them, meaning the Jedi had plenty of reaction time to avoid this.
Revealing mistake: After the battle between Obi-Wan and Anakin/Darth Vader, Vader lies badly burned on the ground slowly crawling up. Palpatine's shuttle flies by, as seen by a shadow. However, even the lava in the shadow turns dark, like the lava is glowing from an external light source instead of glowing within itself. (00:57:50)
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: In the fight scene between Obi-Wan and Grievous, look closely at the lightsabers in Grievous' right hands as he ignites them. The one on top is an Obi-Wan hilt(blue) and the bottom is an Anakin hilt(green). Throughout the fight, these two sabers alternate colors constantly between shots. When Grievous' hand is severed the second time, he drops the Obi-Wan(green) and retains the Anakin(blue).
Continuity mistake: When Anakin, Obi Wan and Palpatine are brought to General Grievous, as they are walking in just as Grievous says "ah yes" Anakin and Obi Wan turn to the left while Palpatine stands a little away from them. When Grievous says "General Kenobi, we've been waiting for you" Anakin and Obi Wan are turning left again.