Visible crew/equipment: In the scene where Rachel is trying to hide Ross from Paul, when he's about to go into Paul's bedroom after he says "Did you really hear a bear?", look at the window behind Rachel when the shot is on her. You can see a large light reflected in the glass and it moves slightly (not just in conjunction with the camera, it moves before the camera shifts).
Continuity mistake: When Phoebe enters the coffee house to get Joey's advice on her outfit for Mike's sister's party, it cuts to Joey saying "You look stop-eating hot", and Phoebe's left hand can be seen making a nervous up-down motion in response. But when it cuts back to her, it is her right hand making the motion and her purse is now in her left hand.
Continuity mistake: In the opening scene in Central Perk when Paul (Elizabeth's dad) takes Ross to one side to talk to him you can see the girl in the blue top enters the door twice: first the shot after Paul says "I'm funny like that" and then again after Ross says "I realise it upsets you".