During a flashback in the Peg Leg mission "The Mad Doctor's Castle", the killer uses a musket. He fires the musket twice without reloading, which is impossible.
During most night scenes, the moon appears both upside down and backwards (incorrectly rotated on both the x- and y-axes.
The game depicts Connor's village being burned down in 1761, which is later revealed to have been done at the order of George Washington. However, by 1761, George Washington had retired from the military and had been living in Virginia for three years.
The musket shown in the game appears to be based on the American Long Rifle, also known as the Kentucky or Pennsylvania rifle. While this weapon was common in the colonies for civilian use at the time, it would not have been used by most military forces apart from militia, and did not have the capability to attach a bayonet. The British Army would have used the "Brown Bess" musket, in service since 1722, of .75 calibre.
After winning the main game, the British leave (except for Templar forts) and US soldiers replace them. However, if you haven't completed the "Liberation Missions", playing them after this will have the US soldiers in place of the British. NPCs will refer to them as "redcoats".
The sea shanty "Haul on the Bowline" is featured prominently in some sequences of the game. This shanty was popular in the 1850s rather than the 1750s-1780s, and actually features references to the American revolution.