The slip-up is in the last big fight in the movie.
Just after Benjamin Martin (Mel Gibson)spears Conl Tavington's (jason Issac)horse causeing him the be throwen off. (Time counter 2h29m09secs)
Benjamin draws a pistol and takes out a lead shot.
The camera give you a close up of the end of the gun,his hand and the shot.
Look close at the barrel. It's rifled.
True rifling dates from the mid-15th century, although the precision required for its effective manufacture kept it out of the hands of infantrymen for another three and a half centuries, when it largely replaced the unrifled musket as the primary infantry weapon.
I hope this is not concitered trivial.