Continuity mistake: Near the end when Rachel runs after Phoebe and Mike to ask Mike if the guy from the bar called, she leaves the apartment with her bag, which she places over her left shoulder. When she is talking to Mike the bag is gone, and then when she returns to the apartment she has her bag again.
Revealing mistake: After Phoebe tells Rachel that Paolo made a pass at her, we see a shot of the outside of Monica's apartment block and Rachel is throwing Paolo's clothes out of the window. Look closely and you can see the clothes have been very badly superimposed on to the background.
Continuity mistake: At the start of the scene in which Ross breaks the little girl's leg, we can see that the stairs are just separated by railings. Later in that scene, when Ross and Chandler start walking up the stairs, there are walls on both sides of them.
Continuity mistake: When Phoebe sits on the swing (when learning to ride her bike), her scarf has one end down her front and the other over her left shoulder. In the next shot, the end is over her right shoulder instead of her left. A couple of shots later, it is switched back again.
Revealing mistake: When Phoebe is looking at the front page of the "Chelsea Reporter," Monica says her restaurant review is on the back page. However, Phoebe doesn't turn to the back page, but merely flips the paper over, looking at the bottom of the front page (and finding the review there).
Continuity mistake: In the one where Rachel is in the hospital after having Emma she is in the bed feeding Emma and Ross is sitting right beside of her. They are talking about their relationship and what should come. If you will watch each shot as they go to showing Rachel's face then Ross's you can see that Rachel's hair in one shot is in front of her shoulder and the next shot it is behind her shoulder. This happens several times.
Revealing mistake: When Joey comes in with the shoebox containing the chick, it looks like a normal sized box, about 5 - 6 inches deep. But when Joey takes the lid off, we can see that the chick must be elevated on something inside the box, since we can see its entire body. Surely, the chick can't be more than 6 inches tall?