The One With The Tiny T-Shirt - S3-E19
Continuity mistake: When Joey and Kate are talking for the first time, a man walks behind Joey and sets down a chair. In the next shot it is gone, and then it is back again. (00:04:30)
The One With All The Jealousy - S3-E12
Continuity mistake: When Monica is confronting Julio about the poem, there are two bottles upside down on the top of others. He turns one over, but in the next shot there are still two upside down, and then there are none. (00:15:35)
The One With The Ultimate Fighting Champion - S3-E24
Continuity mistake: When Chandler's boss is slapping all the guys on the butt, on the side of the table closest to the camera there is a tablet with a pen on it. When the guy comes back in to get his briefcase, the pen is no longer there. (00:20:35)
The One With All The Jealousy - S3-E12
Continuity mistake: When Chandler is showing Rachel his stripper pen, Rachel is sitting with one leg up on the couch. When Ross walks in her legs are crossed, then she takes her leg down off the couch again and crosses them again. (00:18:00)
The One With The Hypnosis Tape - S3-E18
Continuity mistake: When Frank and Alison kiss in the coffee house for the first time, a woman in the background is handed money or something. This is shown twice. (00:04:50)
The One With The Tiny T-Shirt - S3-E19
Continuity mistake: When Chandler is making the Gloria Estefan comment after Joey's dance, he is holding the book flat out with hands on each side. The shot changes and the book is now at a angle. (00:03:30)
The One With The Hypnosis Tape - S3-E18
Continuity mistake: After Mrs Knight sits down with Phoebe's brother in Central Perk, keep an eye on the strap of her handbag. It starts over her shoulder, then moves around and changes position at least half a dozen times. (00:04:40)
The One The Morning After - S3-E16
Continuity mistake: Right before Ross and Rachel storm in, the girls show Joey how much their waxing stuff hurts. Phoebe starts putting the wax on Joey's inner arm, but then the shot changes and she is spreading in on the outer side. Also she slaps the strip on and the blue tab is hanging down off his arm, but then the shot changes again and it is on his arm with the other end of the strip hanging off the other side. (00:11:10)
The One With The Dollhouse - S3-E20
Continuity mistake: When Monica and Phoebe are looking at the dollhouse, Monica says "I don't want a ghost for the house." When she says this, the camera is behind Phoebe whose right hand is up in the air. The shot then changes to Phoebe from the front, and her hand has instantly gone to her lap. (00:04:40)
The One With The Princess Leia Fantasy - S3-E1
Continuity mistake: When Ross and Rachel are arguing about Rachel telling Phoebe about his fantasy, Ross takes a popsicle out of the freezer and bites it. In the next shot, the popsicle is whole again, with no bites, and Ross takes another 'first' bite out of it. (00:11:30)
The One Where Rachel Quits - S3-E10
Continuity mistake: When Rachel's new boss is explaining about coffee, his head moves from the front to the side with no time to do so. (00:20:30)
The One With The Hypnosis Tape - S3-E18
Continuity mistake: Just after Chandler has used the chapstick, in a shot from the side the stick is in his right hand, and then in the next shot he is instantly putting a tissue (which wasn't visible before) up to his lips, and the stick has moved to his left hand. (00:10:45)
Continuity mistake: When they are talking about sperm donation, Joey is eating a cracker with jam on it. Between shots it instantly rotates in his hand. You can tell because the jam goes from being on the top to the bottom side, and because of the way he is holding it you can see there is only jam on one side. (00:14:15)

The One Where No One's Ready - S3-E2
Continuity mistake: When Joey refuses to give Chandler the chair, Phoebe gets hummus on her dress, but in some scenes the stain is much smaller than others. (00:07:00 - 00:08:00)
The One With The Tiny T-Shirt - S3-E19
Continuity mistake: When Joey says "Pete Chicago", there is a green cup on the table next to him; in the shot immediately after that, he is holding it down in front of himself. (00:09:35)
The One With The Screamer - S3-E22
Continuity mistake: When Gunther brings Chandler the cup of coffee from the woman at the bar, Chandler does not take it by the handle; however the shot quickly switches to him holding it by the handle. (00:14:00)
The One With The Hypnosis Tape - S3-E18
Continuity mistake: In the diner scene, Rachel makes the comment about working in fashion and straight men, and her left hand is empty; in a flash, a piece of bread appears without her picking it up. (00:06:40)
The One With The Ultimate Fighting Champion - S3-E24
Continuity mistake: In the scene with Robin Williams and Billy Crystal, there is a shot of Rachel, and her hair is hanging straight down. The next shot of Rachel is from a different angle and there is a section of hair behind her ear; in the shot after that it is hanging straight again, and is then behind her ears again. (00:00:40)
The One With The Flashback - S3-E6
Continuity mistake: When Ross is talking to Phoebe and puts shot glasses on the bar, they're in groups. In the long shot, they're in a straight line then in a closer shot they're in groups again. (00:17:20)

The One Where Monica and Richard Are Just Friends - S3-E13
Continuity mistake: Monica and Richard are squishing tomatoes; when she starts dabbing his shirt with club soda the door behind them leading to Monica's room goes from open to shut between two shots. (00:08:30)
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.