Other mistake: When Phoebe breaks into the other Phoebe's house, after she mentions that the man on the picture is "Chuck Mangionne" the door behind her opens by itself. (00:19:40)
The One With Frank Jr. - S3-E5
Other mistake: Chandler tries to open the door that leads to his room, but Joey has sawed the door in half so only the upper half opens, and Chandler then falls over the bottom half. He has to hit it with some force to fall over it, but it doesn't budge an inch. (00:00:50)
The One With The Football - S3-E9
Other mistake: The accent of the Dutch woman is not a Dutch accent at all. It appears to be Scandinavian. (00:07:00)
The One Where No One's Ready - S3-E2
Other mistake: When Monica beeps into Richard's machine and changes the outgoing message, she always presses the same two buttons when trying to interact with his machine, but gets a different result each time. (00:19:00)
The One With Ross's Thing - S3-E23
Other mistake: When Ross goes to see Guru Saj, he has his 'thing' removed. However, it is really obvious that Guru is not going anywhere near the thing, because you can see that Ross' shirt is still tucked into his trousers, and the Guru just rubs his hands along the shirt. (00:16:35)
The One With Frank Jr. - S3-E5
Other mistake: Monica doesn't realise what the floor looks like under the hamper, but due to her obsessive cleaning she would know this for sure.
The One With The Giant Poking Device - S3-E8
Other mistake: When Monica and Joey are holding containers of Ben and Jerry's, the brand name reads "En and Jer" and other parts of the containers have also been concealed, but we can still recognize the old Wavy Gravy in Monica's hand.
The One With The Flashback - S3-E6
Other mistake: When Phoebe's holding the box of Nabisco Nilla wafers, the Nabisco logo has stickers and paint hiding it and the Nilla is also partially covered so it reads "Villa" wafers.
The One With The Princess Leia Fantasy - S3-E1
Other mistake: When Phoebe makes fun of Ross' Princess Leia fantasy with the rolls, Rachel tries to stop her; the shots used are the same action, just from different angles. Look at Rachel's hands and the towel in her hand when Phoebe puts the rolls by her ears.
The One With The Dollhouse - S3-E20
Other mistake: The dollhouse is only partially burned when Ross takes it into the bathroom to extinguish it. When he shows it to Phoebe it's completely blackened and destroyed. He and Monica wouldn't have just let it burn; they would have extinguished it ASAP, and there's no reason why that wouldn't have been fast if they doused it in the shower.
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.