Continuity mistake: In the beginning in the coffee house, Ross is explaining to Phoebe and Rachel what 'Unagi' is. The blonde lady behind Phoebe is wearing light blue jeans. She then puts a brown leather jacket on, however in the next shot it has gone, only to reappear and disappear again. (00:03:20)
Continuity mistake: Just before Chandler gives Monica the mixed tape, he tries to manipulate a coat hanger into something feasible. He stretches it out and holds it up, saying "Yes, honey, I made it myself," then the camera cuts to another angle as he throws it down. After the cut the hanger is not as stretched as it was before. (00:10:40)
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.