The One with the Sonogram at the End - S1-E2
Continuity mistake: When Monica has her elbow on Ross' hand, her fist is under her chin. The camera changes to a different angle and now her hand is no longer under her chin and to the side of her jaw. (00:12:00)
The One with the Sonogram at the End - S1-E2
Visible crew/equipment: Ross stands up to tell his parents about what has happened with Carol. When he does he walks round the table and stands under a very visible boom microphone. (00:12:05)
The One with the Sonogram at the End - S1-E2
Continuity mistake: Toward the end of the episode, the exterior shot of Central Perk shows about 8-10 people inside the cafe, at the coffee bar, at the tables. But the next interior shot shows the cafe is empty except for our six Friends, lounging in the closed cafe while Rachel cleans up. (00:12:15)
The One with the Sonogram at the End - S1-E2
Continuity mistake: When Barry is explaining how he is an orthodontist, he is holding a dental tool up. Camera cuts and now it's lowered. (00:19:30)
The One with the Sonogram at the End - S1-E2
Factual error: The sonogram shows a fetus that's much too far-developed for Carol's pregnancy. That fetus is at least 20 weeks along. (00:22:00)
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 the Thumb - S1-E3
Continuity mistake: When Ross starts talking about his dog at the start of the episode, Monica has her left foot on the floor and she is holding onto her right leg. As Ross says 'send' both of her feet are on the sofa and her hand is between her legs. (00:01:00)
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 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 Thumb - S1-E3
Audio problem: When Monica is first seen in the kitchen complaining about taking a guy home, the other chef is cutting some items up. However, the audio of the knife clicking as it hits the board is overdubbed. (00:08:00)
The One with the Thumb - S1-E3
Continuity mistake: When Monica ask's Ross if she looks OK, her hand is raised or by her side depending on the shot. (00:09:45)
The One with the Thumb - S1-E3
Continuity mistake: When Rachel says, 'One can never be too Alan, ' we see the stick pom-poms that Ross is holding are up facing Monica, but in the next shot the pom-poms are facing the floor, but after Chandler says 'I personally could have a gallon of Alan' in Monica's closeup we see the stick pom-poms are up again facing Monica. (00:11:30)
The One with the Thumb - S1-E3
Continuity mistake: When Phoebe visits Lizzie, Lizzie is feeding the pigeons with her right hand. In the next shot, a plastic bag has appeared in her left hand from nowhere. (00:11:40)
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 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 Thumb - S1-E3
Continuity mistake: When we first see Chandler in his office, his sleeve is rolled below his elbow. In the next shot, it is above his elbow. (00:12:30)
The One with the Thumb - S1-E3
Continuity mistake: After Chandler shouts at everyone because they are complaining about his smoking, there is an awkward silence and we see a shot of Rachel leaning on the sofa with her arms spread. In the next shot she isn't leaning on the sofa anymore. (00:14:25)
The One with the Thumb - S1-E3
Continuity mistake: When Joey comes into Monica and Rachel's apartment and sits down, he puts his towel on his lap. In the next shot it is over his shoulders, then back on his lap again. (00:18:30)
The One with the Thumb - S1-E3
Continuity mistake: At the end of the episode when Phoebe asks Monica if Alan mentioned them, the towel on the table is next to Phoebe and is untidy. In the next shot, it has moved closer to Chandler and is folded neatly. (00:21:20)
The One with the Thumb - S1-E3
Visible crew/equipment: At the end, just as Monica walks off a tape marker can be seen on the floor where she was stood. This is as the credits are on screen. (00:22:30)
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.