Factual error: Abraham Woodhull did not marry Mary (his cousin) until 1781. The show starts out with him married with a child in 1776.
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.
Mercy Moment Murder Measure - S1-E7
Factual error: Early in the episode, there is a long shot of Woodhull's farm, snow on the ground...and aeroplane vapor trails in the sky.
Men of Blood - S2-E4
Factual error: The show starts out as being November 14th (1777), which was a Friday. However, Abraham tells Ben it's Monday.
Gunpowder, Treason and Plot - S2-E10
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.