Other mistake: To escape from the elevator, Anakin cuts a hole in the ceiling. Later, when they rescue the Chancellor, they almost get crushed by another elevator (it is another one. Each elevator has a number. Obi Wan said the number of this elevator before and it was different than the one that had the hole). However, when a shot of this elevator is shown, it has the same hole that the other elevator has (better seen in slow motion).
Other mistake: During the scene of Anakin's transformation into Darth Vader, there is a close up shot of his face just before his helmet is put in place. All of his face is shown as being badly burned with the exception of his eyelashes, which are still impossibly there. Subjecting one's face to any heat source hot enough to sear one's face will also burn away one's eyelashes as well. (02:01:25)