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.
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.
