The One Where They're Going To PARTY! - S4-E9
Revealing mistake: When Monica and Phoebe are in Central Perk, Phoebe is looking through the list of ideas that Monica has come up with for the use of Phoebe's van. If you look closely (most obvious just after Phoebe says "let's plan the wedding reception") you can see that every single page of the notebook Phoebe is holding has the same thing written on it, instead of lots of different ideas that Monica is meant to have had. (00:17:10)
The One Where They're Going To PARTY! - S4-E9
Revealing mistake: When Phoebe is looking at the front page of the "Chelsea Reporter," Monica says her restaurant review is on the back page. However, Phoebe doesn't turn to the back page, but merely flips the paper over, looking at the bottom of the front page (and finding the review there). (00:07:30)
The One Where They're Going To PARTY! - S4-E9
Continuity mistake: When Joanna stops Rachel from leaving work Rachel's holding her handbag and jacket, and there's still one bag hanging on the wall hook, but when Joanna mentions the "drinking binge" there are two bags hanging from the hook, then it's back to just one bag, yet when Joanna calls Sophie there's nothing on the hook and Rachel has both bags.
The One Where They're Going To PARTY! - S4-E9
Continuity mistake: When Chandler answers the phone and it's Gandalf calling to cancel, Ross is just opening the fridge, but the shot cuts to Chandler with the phone and Ross is putting two beers down on the side next to him - too quick to have got them there from the fridge. (00:05:35)
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.