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.
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.
Revealing mistake: In the beginning of the Five Points battle it happens very often that people get hit badly with a sharp weapon but don't receive any wound. Watch for example in slow-motion how Bill sets out to mow down victim after victim with his cleaver. Later into the fight it becomes a lot bloodier, and sometimes the blood seems to come out of the weapon (e.g Monk's club seems to have a generous blood reservoir).
Revealing mistake: When Amsterdam meets Bill for the first time as an adult Bill is playing Whist. Because he is pissed with a guy whose bet isn't high enough he pulls his knife and pins the man's hand to the table. When he does so the hand isn't anywhere near the point where the knife goes in, and when Bill pulls out the knife again you see that it was stuck in the table and the man's hand was resting next to it.