The One with George Stephanopoulos - S1-E4
Visible crew/equipment: When the guy delivers the wrong pizza, in the shot after Monica grabs the pizza box to hand to Phoebe and shouts that they have George's pizza, the tape marks can be seen on the floor with one of them between the delivery guy's feet.
The One with All the Poker - S1-E18
Visible crew/equipment: The friends are all at Ross' place. Marcel (the monkey) is dancing to the music just before they all play poker (before Rachel enters). However, the reflection of the animal trainer directing Marcel is visible in the TV screen. (00:11:45)
The One with the Dozen Lasagnas - S1-E12
Visible crew/equipment: When Rachel's dumping all of Paolo's clothes over the side of the balcony, we can see the apartment's back wall is only half a wall, with the sound stage and equipment at the left side of the screen.
The One with the Monkey - S1-E10
Visible crew/equipment: While Phoebe's talking about David she mentions the movie 'An Officer and a Gentleman, ' and when she tells them that David is kind of like the guy she went with to see that movie, in the following wideshot the boom mic can be seen moving around at the top of the screen. (00:06:10)
The One with the Monkey - S1-E10
Visible crew/equipment: When Joey walks into Monica's apartment dressed as an elf, just as he takes off his coat we can see stage lighting at the top left side of the screen, above the large dangling star.
The One Where Rachel Finds Out - S1-E24
Visible crew/equipment: After Monica asks Rachel if there's someone else and shouts, "Why the hell are you dumping my brother?," when it cuts to Chandler sitting at the counter, the edge of the set can be seen at the left side of the screen, and also note the front door is wide open for the camera access. Additionally, when Joey joins Chandler at the counter the juice box has black tape covering its brand name.
The One Where the Monkey Gets Away - S1-E19
Visible crew/equipment: When everyone walks in while Ross and Rachel are talking, just as Joey says that he doesn't need violence to enjoy a movie, in the small mirror behind Joey we can see the reflection of equipment moving, presumably a reflector screen.
The One with the Sonogram at the End - S1-E2
Visible crew/equipment: When Ross announces that Carol's pregnant, after Chandler says, "Kind of puts that whole pillow thing in perspective..." in the next shot of Ross and Monica we can see a crew member's sleeve at the left side of the screen. (00:07:30)
The One with the East German Laundry Detergent - S1-E5
Visible crew/equipment: When the horrible woman enters, the boom mike is visible in the mirror at the top of the screen. (00:10:10)
The One with the East German Laundry Detergent - S1-E5
Visible crew/equipment: While Chandler is trying to break up with Janice, and Phoebe comes to help, a cameraman is visible in the background (outside of Central Perk) walking from right to left. The camera cuts away from the window angle, then cuts back, showing another cameraman walking from left to right. (00:19:15)
The One with George Stephanopoulos - S1-E4
Visible crew/equipment: When Monica's looking out the window at George Stephanopoulos with the binoculars, the end of the set wall and overhead studio lighting can be seen at the left side of the screen. (00:15:20)
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 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 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 Ick Factor - S1-E22
Visible crew/equipment: In the scene when Rachel is sleeping next to Ross, you can see part of the mattress behind the sofa which cushions his fall later on when he trips. (00:20:40 - 00:22:55)
The One Where Rachel Finds Out - S1-E24
Visible crew/equipment: When Rachel is on the balcony with her date, after she kisses Ross and says, "Wow!", the shot changes back to her date. While he is saying, "Exactly" you can see a camera man on the left side of the screen. Then when the shot changes to show Rachel and her date you can see him move out of the shot. (00:19:45)
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.