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.
Continuity mistake: Look very closely when Mr. Thomson is taking the vote by a show of hands on whether or not to make the vote on independence unanimous. Of the delegates who say nay, Thomson points to the direction of Adams first, however, Hopkins is the first delegate shown. Thomson points to the direction of Hopkins last, but Adams is the last delegate shown. Maybe this part was reversed, or the filmmakers screwed up.