Factual error: The Liberty Bell is depicted ringing as the Declaration of Independence is being signed on July 4 (a mistake itself) in the film. The bell actually did not ring on that date, but on July 8, when the Declaration had been returned from the printer and unveiled to the public.
Revealing mistake: At one point when the soldiers are walking through the jungle, one of them steps into a trap and is pulled up into the trees to be killed by Indians. However, if you watch this scene carefully, when the soldier (who steps into the trap) walks into frame you can see a wire already attached to his foot leading up into the trees. He doesn't step into a trap. (00:22:26)