Factual error: The Battle of Monmouth is shown. There are no leaves on the trees even though the battle was fought in June. In fact it was so hot there were more British casualties from the heat than from battle. It looks like it was filmed on a very cold day in autumn.
Continuity mistake: When Judge Woodhull is shot and falls to the ground, his and Abraham's positions keep changing depending on the shot. In one shot the Judge will be on his side, but on his back in the next. And Abraham has both hands on his father's wound, and in the next shot, one on his father's upper chest.
Factual error: In the opening credits when the flag waves and (after the AMC logo) one side is American and the other British, the American flag is the correct version of the flag adopted by Congress on June 14, 1777 (though there were versions with six pointed stars and versions with five, the so-called Betsy Ross version). However, the version of the Union Jack is incorrect: it includes the Red Saltire of St Patrick's cross which was not added to the flag of Union until 1801.
Other mistake: Simcoe is in a shop with several other redcoats. They are making jokes at him. He receives a package with a knife inside. While he is inspecting the knife one of the off camera soldiers that is joking makes the screeching sound from Psycho. I though I was hearing things at first and replayed it to make sure. (03:41:00)
Deliberate mistake: When Abraham throws the secret note into the fire, he crumples it up before tossing it in. But then we see a shot of the note lying open and flat on the log before burning. Not only would the note not be able to uncrumple itself, it shows no sign of being crumpled in the first place. This was obviously done deliberately so the audience could read the note one last time.