Bill: Everything you see belongs to me, to one degree or another. The beggars and newsboys and quick thieves here in Paradise, the sailor dives and gin mills and blind tigers on the waterfront, the anglers and amusers, the she-hes and the Chinks. Everybody owes, everybody pays. Because that's how you stand up against the rising of the tide.
At the end of the film you see two gravestones, "Priest" Vallon and William Cutting. Behind them is a river, with a view of lower Manhattan after that. You see a bridge being built,and the city growing and changing. The two men had to have been buried in Brooklyn, rather than Manhattan for this view. See more...
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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: 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: 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: 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.