The One with the Blackout - S1-E7
Revealing mistake: When Phoebe says something like, "Look, the last candle is about to go out", she starts counting down, saying "-47,-48..." and you can see Monica looking at the candle. But there is a light source behind her (it can't be a candle because she is looking at the last candle). (00:20:05)
The One with the Thumb - S1-E3
Continuity mistake: When Phoebe sees Lizzie, she is sat near her trolley feeding pigeons which are out of shot. In the next shot two pigeons have appeared next to the trolley. (00:11:40)
The One with Two Parts: Part 1 - S1-E16
Continuity mistake: Just after Marcel switches the TV to "SAP," Joey comes back and tells Chandler about Ursula and how she gave him extra food. Chandler is holding a bottle of water, and before the camera cuts to Joey it is open, but when he is talking it is capped, and finally when Chandler says "Score," the bottle is open again. (00:07:05)
The One with the East German Laundry Detergent - S1-E5
Continuity mistake: When Joey and Angela talk in Central Perk, the black waitress with long hair is visible the background of shots of Angela. When we see shots of Joey the same waitress is also behind him near Gunther. She is in two places at once. (00:05:50)
The One with All the Poker - S1-E18
Revealing mistake: When Rachel is doing the shuffling trick, it is clear that it is a trick deck. The cards, whilst flying from one hand to the other, change the angle of flight in mid-air, and some of them even move backwards as she moves her hands further apart from each other. This could only happen if the cards were connected to each other. (00:13:20)
The One with the Fake Monica - S1-E21
Revealing mistake: In the scene when Marcel has to get on the plane. It is obvious that David Schwimmer is just shaking his leg and Marcel is doing nothing besides sit on David's foot. It is especially obvious in the second shot. (00:20:45)
The One with George Stephanopoulos - S1-E4
Visible crew/equipment: When Monica climbs out the window with the pitcher of Tiki Death Punch while Rachel and Phoebe are on the balcony, we can see the end of the set wall inside and a crew member moving around back there.
The One with the Ick Factor - S1-E22
Visible crew/equipment: After Ethan and Monica talk about "at gunpoint" being a place, when Monica asks Ethan to stay over it cuts to a shot facing Ethan and we can see that the back wall is less than half a wall.
The One with the Thumb - S1-E3
Continuity mistake: When Monica is first explaining to her friend in the restaurant that her friends don't like anyone she dates, she is putting food onto a plate. The food changes between shots.
The One with the East German Laundry Detergent - S1-E5
Continuity mistake: When Rachel says 'everything looks like jammies now' she is holding up a t shirt. In the next shot as she throws it down, it is now folded up. (00:17:00)
The One with the East German Laundry Detergent - S1-E5
Continuity mistake: When Rachel is holding the ice pack to Ross's head at the end of the episode, Ross' left hand is lowered, then in the next shot, it is raised to his head. (00:21:35)
The One with the Thumb - S1-E3
Continuity mistake: When Lizzie holds the tin foil hat up to Phoebe, in one shot she holds it out with one hand, then in the next shot she is holding it in both hands. (00:12:10)
The One with the Sonogram at the End - S1-E2
Continuity mistake: When Rachel asks Phoebe if she is a twin, she is wiping the table next to her. In the next shot Rachel has her hands together. (00:11:40)
The One with the Dozen Lasagnas - S1-E12
Continuity mistake: During the scene where Phoebe is telling Rachel that Paolo made a pass at her, Rachel unrolls a long length of kitchen roll. During the scene there is a shot over her shoulder where we see that the kitchen roll is as normal and in the next shot we see it unrolled again. (00:15:30)
The One Where the Monkey Gets Away - S1-E19
Continuity mistake: After Ross asks Marcel to bring him the rice, he picks up his chopsticks. In the next shot, he is holding a napkin. (00:02:15)
The One with the Fake Monica - S1-E21
Continuity mistake: When the girls are at the dance club Rachel has a watch on, and it appears and disappears throughout the scene. (00:05:15 - 00:06:15)
The One with the Sonogram at the End - S1-E2
Continuity mistake: At the start of the episode when Chandler is talking about Pink Floyd, his legs are both on the table. When the shot changes, his right leg is resting on his left knee. (00:00:50)
The One with the Dozen Lasagnas - S1-E12
Visible crew/equipment: When Chandler and Joey are talking about buying a table, a line of stage lights is visible in the tv. (00:07:25)
The One with the Thumb - S1-E3
Continuity mistake: When Chandler says he won't quit smoking, he holds his hands out. In the next shot, they are lowered between his legs. (00:06:00)
The One with the Dozen Lasagnas - S1-E12
Continuity mistake: In The One Where Ross Finds Out he's having a boy (series 1), just before Rachel lets it slip, she is sitting on the edge of a chair eating a cookie. Watch her dress, it changes back and forth from being undone from the waist up, to only having two buttons open at the top. (00:19:55)
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.