Continuity mistake: When Monica is standing in front of Phoebe, asking if the smell from Joey's is bothering her, the shots of Monica from the front show her arms held out in front of her, but when the shot changes her arms are crossed. This happens twice.
Other mistake: There are two mistakes in the scene where Phoebe spots Joey's picture in the laundromat. For one thing, when Phoebe says "Oh, here it is", she is looking in the opposite direction of the picture. Also, when she says this, her mouth doesn't move at all.
Continuity mistake: In Joanna's office, Chandler and Rachel are pulling his pants from one another while he is cuffed to the filing cabinet. Right before Rachel says "What if I clean your bathroom for a month?" she throws the pants onto a chair, but then when Chandler later says "Freedom. I want my freedom. Why won't you hear me?" he opens the door to yell to Sophie and they are both holding the pants again.
Continuity mistake: When we first see Ross at the museum, the woman he works with is holding a rock. In the first shot, she is holding onto it with her right hand at the bottom and just before the shot changes she turns away from Ross. In the next shot, she is facing Ross again and her right hand has moved on top of the rock.
Continuity mistake: When Charlie tells Ross about the Met, Ross goes sitting next to her, and his hands are empty when he says: 'Joey really knows his art, huh?'When Charlie says: 'Not so much' Ross suddenly holds a book in his hands. Then, when the shot changes, the book is gone again. It keeps (dis)appearing during the scene.
Factual error: When Monica is in the bath with Chandler, Joey comes in twice, forcing Monica to hide under the bubbles: first he asks Chandler if he wants some chicken, then again when Chandler calls him back and Chandler's giving Monica's order, with Monica still hidden under the bubbles. Somehow, Monica supposedly hears Chandler requesting a soda and nudges or pulls him or something to indicate he was going to get the wrong kind. But no way she could hear him under the water (stick your head in a tub and have your friend recite the alphabet, and see what I mean).