Deliberate mistake: The priest that Ray kills doesn't stagger out of the confessional booth toward the little boy until he's already been shot twice, yet when Ray sees the boy he accidentally shot, he is still kneeling in the prayer position and therefore did not move or react whatsoever to the first few gunshots only a few feet away.
Factual error: Harry is supposed to have loaded his gun with expanding bullets before shooting Ray. Then the bullets are supposed to have gone through Ray, causing minimal damage, before blowing Jimmy the dwarf's head off. In reality, the bullets would have expanded upon impact with Ray, tearing up his torso and certainly killing him after the number of shots that he took. If any bullet fragments were to escape and hit Jimmy, they would not have caused the kind of damage depicted.
Factual error: In the scene where Ray got shot by Harry (Ray kneels on the deck of a canal boat) he instantly starts heavily bleeding through his coat milliseconds after the shot. He has just been hit and still gets pushed backwards by the shot, but he is already bleeding. That's unreal: the coat will be soaked with blood and even that will take a while. But here the blood runs in streams out of Ray's body. Of course he would lose loads of blood if the heart or a blood vessel were hit.