The One With The Apothecary Table - S6-E11
Visible crew/equipment: After Ross and Rachel cover the table with the sheet, when Phoebe walks in Rachel says they can turn out the lights and watch the movie, and in the next shot we can see the end of the set wall, the soundstage and a crew member's leg.
The One Where Ross Dates a Student - S6-E18
Visible crew/equipment: While Phoebe and Rachel are with Monica in the guestroom, Phoebe decides that Rachel should be the one to get the nice room, and right before Monica tells Rachel that she's the first guest at "Hotel Monica" we can see the end of the bedroom set wall, with the kitchen and living room visible.
The One With Rachel's Date - S8-E5
Visible crew/equipment: When Ross shows up at Chandler's office and they both head out to go to the Hard Rock Cafe, just as Chandler walks out the door we can see the edge of the right wall set, allowing us to see the hallway Chandler just walked into and even Chandler's arm.
The One With The Birth Mother - S10-E9
Visible crew/equipment: When Joey's telling Phoebe about having been at a nice restaurant with his date and how she took fries off his plate, in the shots facing Joey in the restaurant we can see the end of the set wall, with a 2x4 framed plywood board and a heavy duty extension cord hanging there.
Visible crew/equipment: During the scene when Phoebe breaks into the other Phoebe's house and gets caught, the older Phoebe was telling the younger one that the man in the photo is not Frank Buffay, but is Chuck Mangioni. Right after that, as Phoebe 2 walks towards the camera, you can see that the door behind her moves open, and there is a visible shadow of someone who walks by that doorway. (00:19:00)
The One Where Phoebe Runs - S6-E7
Visible crew/equipment: When Phoebe bends over to tie her shoelace before the first run, and later when she surprises Rachel at the park while running, the mic pack bulge under Phoebe's top can be seen on her back, and when Rachel bends over there's a bulge at her back as well. It's also a bit noticeable the third time they run.
The One In Vegas, Part 1 - S5-E23
Visible crew/equipment: After Phoebe tells Chandler that Monica wants to make up and that he needs to find her, when Chandler leaves the room we can see the end of the set wall, with the hallway and another hotel room door, at the left side of the screen.
The One With The Donor - S9-E22
Visible crew/equipment: After Chandler explains to Monica why he brought Zack home, just as Chandler leans over the couch to hand Zack the bottle of beer, the camera and a crew member can be seen at the left side of the screen.
The One With Ross's Teeth - S6-E8
Visible crew/equipment: When Joey's in the kitchen holding a football waiting for Janine to come home, so he can talk to her about getting rid of the girly stuff, just as Janine walks into the apartment the camera can be seen at the right side of the screen.
The One With The Video Tape - S8-E4
Visible crew/equipment: While Ross is talking into Joey's video camera, just as Rachel startles him and walks into the apartment we can see the holes in the walls of both apartments, 19 and 20.
The One With Ross's Tan - S10-E3
Visible crew/equipment: When Monica walks into the apartment and announces to Chandler that they're not friends with Phoebe anymore, the hole in the wall beside the door (which is usually hidden behind the picture) can be seen when she walks in and also when Phoebe and Amanda walk in.
The One With Ross's Tan - S10-E3
Visible crew/equipment: After Ross goes in for his disastrous tan, when it cuts to Joey and Rachel walking into their apartment the hole (used for a camera angle) in the wall can be seen at the right side of the screen. As an aside, when Ross leaves Monica and Chandler's apartment later just as Rachel walks in, that hole is seen in the hallway and it's covered up.
The One Without The Ski Trip - S3-E17
Visible crew/equipment: At the end of the scene where Ross buys the group gas at the rest stop, as the shot moves out on Ross leaning against Carol's car you can see the cameraman (and his camera) to the left of the screen. [Widescreen HD version only] (00:19:35)
The One With Ross's Wedding, part 1 - S4-E23
Visible crew/equipment: At the start of the first exterior shot of the London Marriott Hotel, when the camera pans to the left and reaches the awning the reflection of the camera/crane can be seen, and we also see it turn and lower.
The One Where Ross and Rachel...You Know - S2-E15
Visible crew/equipment: At the start, when Chandler and Joey sink into their new Barcaloungers and proceed to recline, the camera can be seen at the right side of the screen. This can also be seen in the show's intro in later episodes. Additionally, set lighting was reflected on the TV screen earlier when Chandler had mentioned "Green Acres."
The One Where Joey Speaks French - S10-E13
Visible crew/equipment: After Rachel tells the others that her father had a heart attack and Ross takes two of Monica's cookies, when it cuts to the shot of Central Perk it's from a low angle, and the studio lighting rigs at the ceiling can be seen through the windows.
The One With The 'Cuffs - S4-E3
Visible crew/equipment: While Joey's scraping gum from underneath the table there's a knock at the door, and when he gets up to head to the door the end of the set wall can be seen at the right side of the screen.
The One With The Ring - S6-E23
Visible crew/equipment: In the opening shot of Phoebe and Chandler in the "nine millionth" jewelry store looking for a ring, at the top of the screen we can see the tip of the boom mic moving in the wideshot. Then, just as Chandler looks into the display case and says, "Ugly ring. Ugly ring. Ugly ring," the boom microphone can be seen moving around in the case mirror's reflection behind him (edited out of HBO Max version).
The One With Joey's Fridge - S6-E19
Visible crew/equipment: After Ross nervously sputters Professor Friesen's name as "Fee-sen-stin-linder" when he walks in on Ross with Elizabeth, it then cuts to Ross, Chandler, and Joey walking into Joey's apartment, and we can see the opening in the wall where the bulletin board usually hangs.
The One In Vegas, Part 2 - S5-E24
Visible crew/equipment: At the start of the Netflix version, when the recap scenes from 5x23 Part 1 are being shown, in the shot of Phoebe, Monica, and Chandler on the airplane the end of the cabin set can be seen beside Chandler, at the right side of the screen.
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.