Continuity mistake: The number of the flats near the start of the first series was 4 and 5. After a few shows they changed to 19 and 20. [The producers realised that the numbers 4 and 5 were for apartments on the lower floors and had shown Monica's apartment to be much higher up so they changed the numbers - it's still a mistake but there's the reason.]
Continuity mistake: In the pilot episode, the guy Rachel left at the altar is called Barry Finkle. In all the other episodes his name is Barry Farber.
Continuity mistake: Mr Heckles's apartment number changes from 8 to 5.
Other mistake: In the first shot of Central Perk in "The One with the Monkey" and "The One with the Dozen Lasagnas", the same footage has been used twice because the same three people are having the same conversation in both episodes.
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.