Continuity mistake: When the barman pulls Ken a fresh pint, the pint is placed on the bar and the glass is not entirely full. The camera changes angle and the glass is now full.
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.
Ken: You coming up?
Ray: What's up there?
Ken: Well, the view.
Ray: The view of what? The view of down here? I can see that down here.
Ken: Ray, you're about the worst tourist in the whole world!
Ray: Ken, I grew up in Dublin. I love Dublin. If I'd grown up on a farm, and was retarded, Bruges might impress me. But I didn't, so it doesn't!