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).
Other mistake: In the episode with Ross's wedding to Emily, Joey is talking on a cell phone with Phoebe as he walks down the aisle. Joey holds the phone out to Ross saying 'it's Phoebe', and one can clearly see that the phone's screen is completely blank. The phone isn't even turned on.
Plot hole: Judy says that both her parents died very young. However, we saw her mother's death in "The One Where Nana Dies Twice" and she was quite old. Also, in Season 7, 'TOW Phoebe's cookies', Jack Geller tells Chandler that his father in law still thinks he is a lawyer and says "So if you ever see me giving them legal advice, just nod along," implying that Judy's parents were both still alive.
Continuity mistake: In the one where Chandler watches the video of a woman giving birth, he takes a video out of the VCR and places it on the table (he's staring at the box and when Monica moves it we hear that a tape's inside). When Monica enters the room, she asks him what he is so upset about and he presses play on the remote control. The tape immediately starts playing, despite no-one moving to put it in the player.
Continuity mistake: When the Snippy Guy is pointing out couples to go on the platforms next, he points to one couple with his left hand, while holding a clipboard in his right hand. In the very next shot he points to the next couple, but this time with his right hand while holding the clipboard in his left.