Factual error: In a scene set in 1862 or 1863 Bill the Butcher says: 'An Irishman will do for a nickel what a ****** will do for a dime or a white man for a quarter'. The first nickel 5 cent piece was coined in 1866. At the time of the scene the 5 cent coin was a small silver coin called a half-dime.
Other mistake: Towards the end of the movie, when the mobs are breaking into stores/houses, the police come to try and stop them. The mob starts to throw rocks at the police. You can see one of these rocks, which look like they should be heavy, bounce right off of one of the officers' heads, and just bounce around as it hits the ground, like it weighs nothing at all.
Continuity mistake: When Amsterdam arrives in New York City and is talking to his new friend, the bag he is holding switches from being held under his arm (camera shot from front) to being carried on his back (camera shot from the back). This happens at least four times in a row during the same scene.
Continuity mistake: As someone pointed out earlier, the poster for the commemoration of the Five Points battle claims to be the 16th anniversary, but the date shows 1863 -- 17 years after the 1846 battle. To further add to the confusion, when William Cutting is talking to Amsterdam in the bedroom after the night at the brothel, he says, "I killed the last honorable man [Priest Vallon] 15 years ago [in the Five Points battle]." So which is it? 15, 16, or 17 years?
Revealing mistake: The scene where Amsterdam and Jenny are in the room together above the tavern, shortly after Bill's assassination attempt, Amsterdam pushes Jenny up against a 12 inch by 12 inch wooden beam. The problem is when he is pushing her up against this beam, you can see it flexing with the weight. Then Amsterdam is holding the beam, you can see that the beam is some type of cloth because the slight touch of his hand makes it dent in.
Continuity mistake: At their first encounter after Amsterdam's return to New York, Bill asks him to come closer. Amsterdam comes around the post he was leaning on, then the camera cuts to Priest Vallon's picture, and when Bill says it's close enough you see Amsterdam coming around the same post again.
Revealing mistake: In the scene where Bill has Amsterdam on the table, he begins headbutting him. You don't even have to look closely to see that Amsterdam's head is obviously just a dummy head with hair sewn on it. You can even see Bill headbutting it, and the head bends a significant amount, just like rubber. If it were Amsterdam's actual head his skull would be shattered in several places and he'd be killed instantly.