The One with George Stephanopoulos - S1-E4
Continuity mistake: When Rachel's friend who is pregnant appears in Central Perk, she says she's like a Duplex. When she does, her left-hand goes from outstretched to on her belly. (00:06:10)
The One Where Monica Gets a Roommate - S1-E1
Audio problem: When Phoebe says "I just don't want her to go through what I went through with Carl" the camera cuts to Chandler's reaction. When you look at the bottom Phoebe's mouth is moving even though she's not speaking. (00:01:39)
The One Where Monica Gets a Roommate - S1-E1
Continuity mistake: When Ross shows Chandler and Joey the can of "Carol's favorite beer" it's unopened as Ross makes a crack about how he "should have known," but in the next shot we see Ross lifting the can and drinking from it, even though he never actually pulled open the stay-tab between the two shots (viewed in widescreen). [In the extended version of the episode you see Ross open the can before taking a drink. In the standard version, the mistake is valid]. (00:09:55)
The One Where Monica Gets a Roommate - S1-E1
Continuity mistake: Before Monica stomps on Paul's watch, the chair closest to the fridge does not have fabric backing, then when Ross eats the Oreo and walks toward his jacket the chair closest to the fridge is now fabric backed and his jacket hangs from a chair with no fabric, plus there are only four chairs around the table. However, when Ross picks up his jacket this chair is now fabric backed, the chair closest to the fridge doesn't have a fabric back yet again, and there are now five chairs around the table. (00:27:00)
The One with the Evil Orthodontist - S1-E20
Continuity mistake: When Rachel's in Barry's office her black handbag is hanging over the counter, but after Billy walks in on them and Barry pretends to look in Rachel's mouth, the bag's lying on the counter.
The One with the Evil Orthodontist - S1-E20
Continuity mistake: When Rachel walks into Central Perk she puts her black handbag down behind the couch and proceeds to talk about Barry, but after Ross smacks Chandler's arm to prompt him to speak up, the handbag's strap appears on Rachel's wrist.
The One with the Sonogram at the End - S1-E2
Continuity mistake: When Monica holds the glass pan of lasagna up over her head to try and find Rachel's ring, when it cuts to the next shot the lasagna is still in the air, but it's different - note burned corners, etc. (00:06:10)
The One with George Stephanopoulos - S1-E4
Continuity mistake: When Ross wrestles his puck away from the little kid in the emergency room, it goes flying at the receptionist. The shot cuts, and it hits her from a completely different angle.
The One with the Stoned Guy - S1-E15
Continuity mistake: When Chandler says Ross isn't speaking metaphorically, he gestures with his right hand. In the next shot, both his hands are in his pockets. (00:06:05)
The One with Two Parts: Part 1 - S1-E16
Visible crew/equipment: Just after the credits, before we see a close up of Ross, a boom mic appears at the top of the screen in the centre of the window on the right. (00:01:30)
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)
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.