The One with All the Poker - S1-E18
Continuity mistake: After the game at Ross' apartment Chandler takes Phoebe's cursed money, and when Ross wants to settle up with "the big Green poker machine who owes fifteen," Rachel's sitting down at the table in front of Ross, but then it cuts to Rachel who's suddenly standing up near the table. (00:12:30)
The One with All the Poker - S1-E18
Visible crew/equipment: After Rachel gets the call that she did not get the job, when she places the five dollar bet and asks if anyone has a problem with that, in the next wideshot as everyone says, "NO!" the reflection of moving equipment can be seen in the window behind Monica.
The One Where Rachel Finds Out - S1-E24
Visible crew/equipment: When Rachel leaves the apartment to catch Ross before his flight, just as she opens the door a crew member's sleeve and equipment are visible at the left side of the screen.
The One with the Fake Monica - S1-E21
Visible crew/equipment: While they're all looking at Monica's credit card statements, when Ross tells Marcel to stop humping the lamp and also when Marcel runs off to Rachel's bedroom, the reflection of the ceiling's studio lighting rigs can be seen on the TV screen.
The One with the Evil Orthodontist - S1-E20
Visible crew/equipment: While Chandler's sitting at the table waiting for the phone to ring, Joey rushes into the apartment because of telescope guy, and when Rachel walks out of her bedroom the reflection of studio lighting rigs can be seen at the top of Monica's TV screen.
The One with the East German Laundry Detergent - S1-E5
Continuity mistake: While Rachel and Ross are at the laundromat there's laundry detergent, softener, bleach, etc., atop the soda machine, some of which change position or vanish in consecutive shots.
The One Where the Monkey Gets Away - S1-E19
Continuity mistake: When Rachel and Ross are in the apartment with Marcel, who's still wearing the pink tutu, the bottle of wine can be seen on the side table beside the teapot, but when Ross remembers the wine it's now between the teapot and the couch.
The One Where the Monkey Gets Away - S1-E19
Continuity mistake: When Monica takes the newsletter from Rachel it's open to the pages with engagement news, and we can see the left page has pictures as Monica reads Mindy and Barry's notice on the right page, but when Monica wiggles out of her comment about Mindy being pretty that left page is now only words at the bottom, even though she's still open to the same page with Mindy and Barry's notice.
The One with George Stephanopoulos - S1-E4
Visible crew/equipment: At the end, while Rachel's on the phone talking about the Visa card, in the shots facing Monica, Phoebe, Joey, and Chandler when they're playing Twister, the end of the set wall can be seen at the right side of the screen. (00:15:10)
The One with the Sonogram at the End - S1-E2
Visible crew/equipment: While Rachel's looking for the ring she says, "Now I'm gonna have to return the ring, without the ring, which makes it so much harder," and at the start of the next shot the reflection of a screen can be seen moving on the window behind Monica. (00:05:55)
The One with the Dozen Lasagnas - S1-E12
Continuity mistake: In the scene where Phoebe confesses to the gang that Paolo made a pass at her, it is pitch black outside. When Joey and Chandler turn around after heading for the door, it is sunny outside.
The One Where Underdog Gets Away - S1-E9
Visible crew/equipment: When Joey walks into Central Perk and everyone's laughing about the VD ads, just as Phoebe comments that laughing can be "infectious" we can see the camera at the right side of the screen.
The One with the Dozen Lasagnas - S1-E12
Continuity mistake: When Ross says he could escape from any uterus, Joey is holding two small books. In the next shot they have vanished and he is holding a large book. (00:02:10)
The One Where Underdog Gets Away - S1-E9
Continuity mistake: Chandler is able to get into Monica's apartment to tell everyone that Underdog got away, but later when Rachel closes the door it is now locked. We can see the door as each person is leaving and nobody does anything which could be construed as locking the door before it closes. It's been often demonstrated in the show that the door doesn't lock automatically. (00:13:20)
The One with George Stephanopoulos - S1-E4
Continuity mistake: Just before Ross gets hit in the hockey game, you can see him wearing a foam finger which then disappears. (00:11:45)
The One with Two Parts: Part 1 - S1-E16
Revealing mistake: If you look closely you can see that the name of the restaurant "Riff's" is printed on by computer in post-production. (00:00:05)
The One with the Ick Factor - S1-E22
Continuity mistake: Monica is in her apartment with her boyfriend and they are kissing, and she invites him to stay the night. Watch the glass of wine she has poured herself: the amount of wine in the glass keeps changing. (00:08:45)
The One with the Blackout - S1-E7
Continuity mistake: In the scene where Joey is standing with candelight over Ross' neck, the candle is full length, but in the next shot it's only half length. (00:13:00)
Continuity mistake: In the scene just before Joey goes into the shower, when he is thanking the director for the opportunity, the camera shot goes back and forth between Joey and the director several times. During this series of shots, the part in Joey's hair switches sides nearly every time. It appears that the entire shot is reversed - in the closeup, the shower curtain is on his left and the shadow to his right is sharply focused. In the lower (long) shot, the curtain is to his right, and the shadow on his left is more focused. (00:13:05)
The One Where Underdog Gets Away - S1-E9
Revealing mistake: Whenever Monica's apartment is shot from the point of view of the balcony looking in, fake walls have to be put up across the room to cover the open space (since there is no wall there usually). When the friends are looking out the window at Ugly Naked Guy and his girlfriend in this episode, you can see that the rear wall does not extend nearly far enough - there is a large black space behind Monica. (00:19:25)
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.