The One With The Giant Poking Device - S3-E8
Factual error: The "very long poking device" that the friends fashion out of chopsticks would never actually work. It has vulnerable points every half-foot or so (the length of the chopsticks) and after a certain point would just break or sag under its own weight at one of the vulnerable points.
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.