The One Where Chandler Doesn't Like Dogs - S7-E8
Deliberate mistake: Monica sees the dog on her settee from Ross's apartment, which wouldn't be possible from the angle as Ross's place is lower than Monica's. (00:04:50)
The One Where Chandler Doesn't Like Dogs - S7-E8
Deliberate mistake: When Phoebe is trying to sneak the dog out of the apartment, the guys say that they have noticed that the bag is moving, yet the bag doesn't move at all. (00:04:10)
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.