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)
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.