The One With a Chick. And a Duck. - S3-E21
Continuity mistake: At the beginning of the episode, Phoebe gives Monica a push on her rollerskates and then we cut to Gunther giving Rachel a mug of cocoa. At this point, Monica is about to crash into Rachel, but as the angle changes we see Phoebe giving Monica a push for a second time.
The One Without The Ski Trip - S3-E17
Continuity mistake: When Phoebe is saying how she gets out of tickets, she is pointing at herself in one shot and not in the very next shot. (00:05:50)
The One With The Football - S3-E9
Continuity mistake: At the end, Chandler points at Joey, and when he does so, his sleeve goes from rolled down to rolled up instantly. (00:22:10)
The One With The Football - S3-E9
Continuity mistake: Chandler says he's been preparing for something his whole life. When he says this, his right sleeve is rolled up. Camera changes, and now it's rolled down. (00:10:40)
The One With The Football - S3-E9
Continuity mistake: When Joey tells Chandler to prepare to feel very bad about himself, he has the football in his right hand. When the shot changes, it's in his left. (00:10:30)
The One With The Football - S3-E9
Continuity mistake: When Joey introduces himself to the Dutch lady, the way and where he holds the football changes between successive shots. (00:08:40)
The One With The Football - S3-E9
Continuity mistake: When Rachel asks Ross if not catching Joey was part of his football strategy, she has her hands outstretched in one shot and then on Ross' shoulder in the next. (00:07:10)
The One With The Racecar Bed - S3-E7
Continuity mistake: When Monica and Rachel show Ben them banging their heads against the wooden beam in the kitchen, Phoebe is hovering on the phone in the background when she is supposed to be at the dentist's office. (00:14:13)
The One With The Ultimate Fighting Champion - S3-E24
Continuity mistake: Ross buys the Ultimate Fighting Combo, a large pop and popcorn at the fight, but when he and Monica sit down, they are never seen again. Furthermore, when Monica talks to Pete at the ring, you can see that the Combo was not set on the floor.
The One With The Princess Leia Fantasy - S3-E1
Continuity mistake: In the seen where Monica is shouting "why hasn't he called" she is holding a juice bottle, but when the shot cuts to Phoebe she is holding a glass.
The One With Frank Jr. - S3-E5
Continuity mistake: When Frank is trying to melt a spoon there's one shot where he holds the spoon high above the table, then the angle changes and he's pressing the spoon against the plate.
The One Where Ross And Rachel Take A Break - S3-E15
Continuity mistake: When Phoebe rushes in at the start she has a coat on. Camera cuts to Monica then back to Phoebe, and the coat is off. There is not enough time to take it off. (00:00:15)
The One With The Princess Leia Fantasy - S3-E1
Continuity mistake: S3E1; Ross is telling Chandler about how woman tell each other everything in Central perk. Chandler puts a book about trout on the table and then talks to Ross, then the camera zooms out and the book has moved more to his left and a coffee mug is in front of it.
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.