Plot hole: As evidenced by the big bar room shootout, even if they couldn't die in this episode, wounds would still show up on your body (if shot with a gun, there would still be a hole). So, when Peter jumped off the building, when he hit the ground he should have been reduced to a fleshy puddle, even if he weren't dead.
Continuity mistake: When Peter, Anne Frank, and a group of people (presumably Anne Frank's family) are hiding from the Nazis, Anne Frank and her family look over to discover Peter munching crisps. In the next shot, Anne Frank's family look somewhat different, in fact they are a different group of people entirely. (00:06:40)Blibbetyblip
Continuity mistake: When Peter goes to see his ex-girlfriend, she says she never washed her hand and takes off her right glove to show a black hand. It is like this right up until Peter leaves. She then turns around and the hands have switched colours. (00:10:00)Xofer
Continuity mistake: When Francis is standing on a chair, nailing the crucifix above the door, the bottom of the crucifix overlaps onto the door frame, but when Francis comes down from the chair, the bottom of the crucifix is above the door frame.Blibbetyblip