Corrected entry: When Dooku makes the platform collapse on Obi-Wan it is obvious that he is just a dummy, look at the way he slides across the floor with no parts of his body reacting.
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.
Corrected entry: Just before Obi-Wan and Anakin begin their duel, Obi-Wan says "I will do what I must." and removes his lightsaber from his belt. As he is raising his arm above his head he "flicks" the lightsaber hilt as if he has just activated it. Anakin then says "You will try", and Obi-Wan then activates his lightsaber. Obviously it was decided that Obi-Wan should wait until after Anakin delivers his line for Obi-Wan to activate his lightsaber and the timing was simply switched, leaving an awkwardly long time for Obi-Wan to stand there holding a lightsaber in the air that isn't turned on.
Correction: The way he flicks his lightsaber in his hands doesn't really reveal anything. Nor is it a mistake for him to produce his lightsaber like that. The idea that a decision was made to make the lightsaber go on later is just guesswork and the scene doesn't reveal that at all.
Corrected entry: General Grievous, whose two arms can split into four, has a total of twelve fingers (six on each hand when his arms aren't split). However in some shots (such as when he orders his ship's bridge crew to fire the emergency booster engines in an early scene) we can see he has five on each hand when his arms aren't split. In other shots, he has the correct number of fingers.
Correction: In the example that you mentioned, while General Grievous' right hand is mostly out of view, his left hand is seen, with six fingers on it. One of them was probably mistaken for another part of his hand, or a ship in the background.
Corrected entry: In the Mace Windu/Palpatine fight scene, the glass window is shattered after being hit by a lightsaber. However, while Palpatine is talking to Anakin after the fight, you can still see Anakin's reflection in the space where the glass was. (01:18:15)
Correction: That is a building, not a shadow. The building coincidentally looks just Anakin's shadow, but the building is in the background even before Anakin arrives and it doesn't follow his movements. Look closely at the picture and you will see the building in the background when Windu smashes the glass.
Corrected entry: The final scene of the movie shows Vader and the Emperor looking out at the Death Star being constructed. This doesn't fit with the storyline as there is almost 20 years between episodes 3 & 4, that is quite a slow construction. Compare this to the time in which the second and more powerful death star is almost finished. Some time could be accounted for through prototype versions and testing, but not 20 years.
Correction: This has already been covered elsewhere - considering that major building projects on Earth can take several years to complete, it's hardly unreasonable that it could take the Empire, even with their more advanced technology, twenty years to construct a battle station that's seventy-five miles across, involves at least one completely untried technology (the planet-destroying superlaser) and many other technologies on a scale previously unheard of. The second Death Star's construction would be quicker, as they'd have learned from building the first one, but it is quite clearly not even close to being finished - the amount of construction that's seen is quite consistent with a build time of two to three years.
Correction: Besides, the Death Star may not have much steel. Other materials would be present. For example, titanium alloys replace steel on Earth, and composite materials can be substituted for steel in some cases. While steel is strong, lighter materials are better suited for objects that need to be moved.
Correction: His body didn't react because he was completely unconscious.