Factual error: During Memnon's training session, at least one of his opponents uses a Japanese training sword known as a shinai. You can see this most clearly after the fight, when one of the weapons lying on the ground comes into view. Not only did the Egyptians and Japanese not have any contact with each other at this time, but this particular training weapon had not yet been invented.
Factual error: In the very beginning of the movie, when Mathayus rescues Jesup, he fires several arrows at Jesup's would-be executioners, and the targets of these arrows fly backward, across the room, and smash out the side of the building. I don't think I need to go into a detailed discussion of physics on this.