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.
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.
Continuity mistake: When Peter, Quagmire and Cleveland become cops because Joe trains them and they are all at Peter's, Joe has binoculars and is looking across the street and saying he is watching his wife Bonnie in her house. In just about every episode it is stated that Joe and Bonnie's house is right next to Peter's. So why is he looking across the street when their house is next to Peter's?
Continuity mistake: Pay attention to the items behind the police auctioneer. In the first couple of shots we see a statue of a knight on a horse to the left of the auctioneer. When the camera cuts to Peter, and then cuts back, the statue is gone. The statue is then back in the next shot.