Revealing mistake: At the very beginning, as Gunther complains to Joey about talking to his friends, he then says something like, "This guy has been waiting for his coffee for ten minutes". He passes a mug to Joey, but it is very clear the mug is empty. (00:01:40)
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)
Visible crew/equipment: When Chandler points out to Joey that his oblivious comment was made in front of Ross it cuts to a closeup of Ross, and camera equipment can be seen at the right side of the screen, and it's still there in the next two closeups of Ross.
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.