Other mistake: When Lamont walks into the alley to avoid being followed by one of Khan's warriors, he makes himself invisible, and his shadow vanishes as well. It's well noted at the beginning of the film that his shadow is always visible even if he isn't. Therefore, his shadow should still be seen on the ground and give him away.
Other mistake: While Cranston and Shrevnitz discuss Margo Lane, the view through the cab's windshield shows the vehicle heading for a building, but the next shot of Shrevnitz driving shows him making no attempt to turn the cab's steering wheel to avoid the building.
