Continuity mistake: The last time Shakes serves as an altar boy for Father Bobby, he puts the white coat on top of the black gown, and it is all straight. Yet, when he turns to Father Bobby, the coat is lopsided and hangs over his left shoulder, and Father Bobby straightens it again. Even if the coat slides a little when Shakes leans towards the mirror right before turning to Father Bobby, it wouldn't pass his shoulder unless he did it on purpose.
Deliberate mistake: In the scene where the boys scratch off the paint on the window so they can look at the ice skaters getting dressed, there's a grille about 6 inches from the window. When viewed from outside their faces are pressed against the grille, but when the shot changes to inside the building looking at their eyes moving, their eyes are much closer to the window than the grille would allow.
Other mistake: At the end of the film, the narrated epilogue describes the fates of 4 of the principal characters. The narrator first says, "John Reilly's bloated body was found face-up in a tenement building" (suggesting that he was at least a few days into decomposition) following his death by tainted alcohol. This statement is accompanied by a black and white police photo of John Reilly's body; but the photo shows him quite trim and freshly dead, not bloated or discolored at all. The same mistake is made for the next character, Thomas Marcano (who was shot to death). The narrator says Marcano's body "lay undiscovered for more than a week." Once more, the statement is accompanied by a black and white police photo of Thomas Marcano's blood-stained body, which appears freshly deceased with no signs of decomposition whatsoever.