Factual error: When Rachel is boarding the plane to Paris, the plane's right hand side is being used for boarding. However in all airlines all over the world, they always use the left side for boarding. The right side is a 'service' side.
Other mistake: When Joey sat in the paint the first time, there was a mark, but the second time, it didn't leave a mark.
Continuity mistake: After Ross decides to go after Rachel, in the overhead shot all four of the cab's doors are closed, but when it cuts to Ross and Phoebe getting in and shutting their front doors suddenly both back passenger doors are inexplicably wide open, then when Ross shouts about missing seatbelts both back doors are closed again. Then when the guy gets into the back seat he shuts his door, but when he asks for the medallion number both back doors are open, and then they're closed again.
Other mistake: When Rachel attempts to board the plane the first time, the man at the desk looks at her passport upside down.
Character mistake: Even though both Ross and Rachel have cell phones with them and use them for other calls, it never occurs to Ross early on and as he's frantically racing to the airport with Phoebe, to call and tell Rachel that he loves her or at least to say that he is on his way to tell her something important before her plane takes off for Paris.
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.