Continuity mistake: When Rachel and Phoebe are talking in the Baby Beauty Contest and Rachel is holding Emma, Emma's head instantly changes position between shots several times, often going through 180 degrees. Clearly they couldn't get her to do the scene in one take and therefore the editing suffers.
Revealing mistake: At the point in the ceremony where Joey forgets the rings, the camera pans out and you see Chandler step sidewards to get the ring from Ross, and Monica step sidewards to get the ring from Rachel and Phoebe. As Monica moves, her dress slides across and one of her feet is revealed; it has what looks like a brown boot or heavy brown shoe on it.
Revealing mistake: When Phoebe says something like, "Look, the last candle is about to go out", she starts counting down, saying "-47,-48..." and you can see Monica looking at the candle. But there is a light source behind her (it can't be a candle because she is looking at the last candle).
Continuity mistake: Joey goes into the bathroom and the toilet is behind the door. In a previous episode, when Joey doesn't know about Chandler and Monica, he comes out of his room and thinks it is morning. He goes into the bathroom and Chandler pushes the door open to reveal Joey asleep on the toilet with his toothbrush in his mouth, only the toilet is now on the other side of the room, not behind the door.
Continuity mistake: Paul finally opens up, and cries like a baby to Rachel. While talking to her at the Breakfast Bar (when Rachel is trying to distract him with sex), he's wearing a white linen shirt that constantly changes between tear-stained and wrinkled to ironed and clean.