The One With Two Parties - S2-E22
Other mistake: In the scene where Rachel is talking to Chandler in the hall, after she says "the 4th of July", it cuts to a shot from behind Rachel's head. If you look on the right hand side of the screen, you can see a piece of wood in the foreground. This probably came from Joey and Chandler's doorframe, through which this view would have been filmed. In addition, this door was supposed to have been closed throughout the entire duration of this scene. (00:17:55)
The One With Two Parties - S2-E22
Continuity mistake: Just after Rachel goes in to her surprise party in Chandler's apartment, she is talking with Ross and Chandler and says, "Both of them are here?" As she says this, she is facing forwards, yet in the next shot, she is suddenly facing Chandler. (00:08:15)
The One With Two Parties - S2-E22
Continuity mistake: When Chandler and Joey are in Monica's apartment blowing up balloons, Chandler's balloon changes type. The camera changes and it goes from shiny to dull. (00:03:30)
The One With Two Parties - S2-E22
Other mistake: When Ross is at Monica's party getting Mr. Green's glasses and cigarettes he bumps into Mrs. Green and ends up having to come up with an alibi for the glasses and cigarettes. He then puts the glasses on, puts a cigarette in his mouth and says 'In fact I'm gonna go out into the hallway and fire up this bad boy'. At this point he walks past Rachel but he stops still as if frozen mid-step just before the shot cuts to him walking out into the hallway.
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.