The One with the Boobies - S1-E13
Continuity mistake: When Joey finds out that his mother knows about his dad's affair, she tells him she's fine and holds her hands to her chest. In the next shot her hands are outstretched in front of her. (00:17:10)
The One with the Sonogram at the End - S1-E2
Continuity mistake: When Ross arrives at Monica's apartment, both Ross and Monica walk past the beam in the middle of the room. In the next shot as they continue walking they walk past the beam again. (00:07:05)
The One with the Dozen Lasagnas - S1-E12
Continuity mistake: When Ross visits Carol, he hugs her, and puts his hands on her hips. In the next shot, he isn't touching her and has taken a step back instantly. (00:05:10)
The One with the Dozen Lasagnas - S1-E12
Continuity mistake: At the end of the episode, when Monica scores a goal against Joey and Chandler, she is playing with the red team and scores with her strikers. In the next shot, a blue midfielder scores the goal. (00:21:05)
The One with the Fake Monica - S1-E21
Continuity mistake: In the scene when Joey and Chandler come into the cafe to say that Marcel got into San Diego zoo, the man who wants him for animal fighting turns and says that Ross is making a big mistake. At this point the monkey starts to go down Ross's arm and almost drops off but in the next shot he is far up on his shoulder again. (00:14:40)
The One with Two Parts: Part 2 - S1-E17
Continuity mistake: When Ross and Jack are talking about becoming a father, Ross takes a drink out of a glass and puts it back down. The liquid doesn't move when put back down. (00:08:15)
The One with the Monkey - S1-E10
Continuity mistake: When Ross say 'just a smidge' after Rachel says Paulo named her breasts, Phoebe is holding tinsel and Rachel is looking at Ross. In the next shot, Rachel is looking in the opposite direction and the tinsel has vanished from Phoebe's hands. (00:06:00)
The One with the Thumb - S1-E3
Continuity mistake: When Chandler smokes the cigarette at the start of the episode, keep an eye on Joey's arms. First he moves his arms between his legs, then his left arm moves onto his knee between shots. (00:03:45)
The One with the Thumb - S1-E3
Continuity mistake: When Ross said his parents sent their dog away, Chandler is holding onto his right foot with his hand. In the next shot, the foot is gone and his arm is in a different position. (00:01:00)
The One with George Stephanopoulos - S1-E4
Continuity mistake: When Phoebe talks about the cave in in the mine, Ross has his hands in his pocket behind her. In the next shot his hand is on the sofa. (00:04:10)
The One with the Blackout - S1-E7
Continuity mistake: During the Monopoly game (deleted scene), right after Monica says, "we can bring my wheelbarrow, to carry your teeth," we see Ross reading the game manual at the end of the shot. At the beginning of the very next shot, he is suddenly rolling the dice with no manual in his hands. (00:17:00)
The One with the Birth - S1-E23
Continuity mistake: In the scene when Carol is giving birth, there is a shot when Carol shouts "Where were you?" Her trousers are visible under the sheet. (00:16:25)
The One with the Blackout - S1-E7
Continuity mistake: After the light comes back on and Ross is holding his heart after he sees Rachel kissing Paulo, in the next shot when Joey starts speaking to him his hand is by his side. (00:20:40)
The One Where the Monkey Gets Away - S1-E19
Continuity mistake: When Ross comes back to Monica and Rachel's apartment and Rachel tells him she has lost Marcel, he takes off his overcoat and lays it over the back of the sofa and then sits by it. As the scene continues, the sofa is still visible in some shots and the black coat is crumpled up on the sofa cushion. (00:11:25)
The One with Two Parts: Part 2 - S1-E17
Continuity mistake: When Joey is talking to Ross and Chandler about missing Phoebe's birthday, Chandler has the newspaper in his hands. In the next shot, you can see that Chandler does not move at all, then in the next shot, the paper is on the table. (00:04:35)
The One with All the Poker - S1-E18
Continuity mistake: In the scene where Rachel and Ross are playing poker head to head, Rachel borrows $7 from Monica's purse and then puts the purse down on the table. She puts it down on her left hand side but it then switches to her right hand side without her touching it and then back again. (00:22:25)
The One with the Stoned Guy - S1-E15
Continuity mistake: After Chandler walks in on Ross and Joey's dirty talking, Chandler walks towards the door and Joey turns to Ross. In the next shot Joey has turned around and is facing Chandler. (00:13:15)
The One with Two Parts: Part 1 - S1-E16
Continuity mistake: When Ross, Carol and Susan are watching the birth video, Ross has his hand on the fake baby's head. In the next shot his hand is on its shoulder. (00:15:50)
The One with the Stoned Guy - S1-E15
Continuity mistake: When the monkey is hanging off Ross's date's hair, in one shot he is hanging upside down, then in the next he is hanging the right way up. (00:06:35)
The One with the Candy Hearts - S1-E14
Continuity mistake: In the restaurant when Ross asks Carol to join him, his date has her hand with the chopsticks in it up on the table. In the next shot it is gone. (00:14:55)
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.