The One Where Monica Gets a Roommate - S1-E1
Continuity mistake: At the end of the episode when Chandler says "I'm in Las Vegas" Rachel starts to pour his coffee. In the next shot they have moved apart instantly and Chandler is putting his cup down. (00:28:05)
The One with the Sonogram at the End - S1-E2
Continuity mistake: At the very start of the episode, Monica holds up both of her hands. In the next shot her right hand is wrapped around her legs. (00:00:05)
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 Sonogram at the End - S1-E2
Continuity mistake: When we first see Ross at the museum, the woman he works with is holding a rock. In the first shot, she is holding onto it with her right hand at the bottom and just before the shot changes she turns away from Ross. In the next shot, she is facing Ross again and her right hand has moved on top of the rock. (00:02:05)
The One with the Sonogram at the End - S1-E2
Continuity mistake: When Rachel loses the ring near the beginning, Chandler and Joey get off a chair to help look. But then the shot cuts to Monica, and behind her you can see Chandler at the fridge without enough time to get there. (00:05:40)
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 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 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 Sonogram at the End - S1-E2
Continuity mistake: When Monica is asking if Ross has any stories to tell, she is looking at Ross and grinning. When the camera cuts, her expression has changed massively. (00:12:00)
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
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 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
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)
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.