Revealing mistake: When Monica and Rachel apologise to Danny, as he shuts his door for the second time the set wall visibly shakes. (00:07:55)
Continuity mistake: When Rachel is talking to Phoebe about cremating the coat there is a mirror behind her with a laptop reflected in it. The reflection shows it switched on, but in the wider shots it is switched off. (00:09:15)
Continuity mistake: Ross is in his apartment, and he is saying he will miss it. Throughout the scene, the phone appears and disappears from beside the charger cradle. (00:10:10)
Visible crew/equipment: When Ross notices that Ugly Naked Guy is back, in the next exterior shot we can see the top of the set as everyone gathers at the window.
Visible crew/equipment: While everyone's in the apartment Ross is on the balcony talking to Emily on the phone, and in the mirror we can see the reflections of Phoebe and someone else wearing a blue shirt (with a large white pattern) and blue pants (looks like jeans), but none of the others are actually dressed like that.
Visible crew/equipment: Just as Monica and Rachel walk into the storage room, at the start of the shot the camera casts a shadow on the head sculpture which moves as the camera moves.
Continuity mistake: When Rachel and Monica knock on Danny's door and he opens it, there is a wall a few feet behind him. Later, when Rachel shows up at Danny's apartment to cancel their date, she enters into an open room and there is no longer a wall in front of the door. Danny's apartment is supposed to be one floor directly below Chandler and Joey's apartment. This was obviously the same set for their apartment that was used for Danny's and the wall was added for that shot to disguise it.
Continuity mistake: Joey's bedroom door opens and closes as the camera goes between him and Monica and Chandler when he is telling him he doesn't want to see them kissing.
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.