The One With The Ballroom Dancing - S4-E4
Other mistake: Right at the end of the episode, Phoebe's got a job interview. We see the outside of a massage parlour, but the name on the awning has been superimposed - it moves about a bit while the shot itself is still. (00:20:45)
The One With The Ballroom Dancing - S4-E4
Other mistake: In the scene where Rachel is going to take out the trash, Monica tells her the garbage room is the 3rd door on the left. However, when Rachel comes back with the pizza box and Monica leaves for the garbage room, she leaves the apartment and walks towards the right - there are no doors that way, just the stairs. (00:00:50)
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.