The One with the Fake Monica - S1-E21
Visible crew/equipment: While they're all looking at Monica's credit card statements, when Ross tells Marcel to stop humping the lamp and also when Marcel runs off to Rachel's bedroom, the reflection of the ceiling's studio lighting rigs can be seen on the TV screen.
The One with the Fake Monica - S1-E21
Revealing mistake: In the scene when Marcel has to get on the plane. It is obvious that David Schwimmer is just shaking his leg and Marcel is doing nothing besides sit on David's foot. It is especially obvious in the second shot. (00:20:45)
The One with the Fake Monica - S1-E21
Continuity mistake: When the girls are at the dance club Rachel has a watch on, and it appears and disappears throughout the scene. (00:05:15 - 00:06:15)
The One with the Fake Monica - S1-E21
Continuity mistake: When Monica, the fake Monica and Rachel are in the girls' apartment talking about the two Monicas auditioning for CATS, Monica (real) has a baguette and a bowl of sandwich filler on the table. In one shot of all three of them, she opens the baguette and starts filling it, then the camera goes in for a close-up of the real Monica and she opens the same baguette and starts filling it again. (00:10:50)
The One with the Fake Monica - S1-E21
Continuity mistake: In the scene when Joey and Chandler come into the cafe to say that Marcel got into San Diego zoo, the man who wants him for animal fighting turns and says that Ross is making a big mistake. At this point the monkey starts to go down Ross's arm and almost drops off but in the next shot he is far up on his shoulder again. (00:14:40)
The One with the Fake Monica - S1-E21
Visible crew/equipment: After Marcel has humped the chair, when it cuts to Joey walking in saying that there already is a Joseph Stalin, we can see the reflection of a crewmember (presumably female) in the small mirror on the wall who's wearing a black top - and it's not Rachel, the angle is off.
The One with the Fake Monica - S1-E21
Factual error: The monkey is allowed outside his cage at an airport gate. Animals, with the exception of assistance dogs, cannot be transported in the cabin with passengers, and this rule applied in the 1990s as well. There is no way a monkey would be brought through a security checkpoint into a terminal concourse of a NYC airport and allowed aboard a regular commercial airliner.
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.