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.
The One In Vegas, Part 1 - S5-E23
Visible crew/equipment: While Phoebe, Monica, and Chandler are with gladiator Joey in the casino, Joey notices the tension between Chandler and Monica, and when he asks what's going on a tape mark can be seen on the floor at the feet of the extra standing at the slot machine, then more tape marks can be seen at the same spot after Monica sarcastically wishes Chandler happy anniversary.
The One With The Mugging - S9-E15
Visible crew/equipment: When Chandler first walks into the conference room at work, and also later when he walks out of the conference room while using a cane, the end of the set wall can be seen at the left side of the screen.
The One In Massapequa - S8-E18
Revealing mistake: During Jack and Judy Geller's party, there are many shots where Elliott Gould's (Jack Geller) stand-in is perfectly visible. First, when Catherine walks over to offer congratulations to Rachel and Ross. Second, when Ross looks directly at his "dad" to ask if they have to pretend they're married. Then, numerous wide shots of "stand-in Jack" and Judy seated together in the background, such as after Rachel mentions the ring being the size of her fist, and during the toasts, etc. (00:06:00)
The One With All The Wedding Dresses - S4-E20
Continuity mistake: Ross comes into Chandler and Joey's apartment to ask the guys and Rachel what they are doing in four weeks, the Magna Doodle behind him first says "poop", then its screen is blank. We cut to Joey checking his diary, cut back to Ross, and it now has "get out" written on it. [Fullscreen version]. (00:10:35)
The One Where Old Yeller Dies - S2-E20
Visible crew/equipment: Chandler and Joey are spending time with Richard; as they play foosball and Richard scores, he leans back and says "Could that shot BE any prettier?" in a mockery of Chandler. The end of the wall and the hallway behind it are visible (ie the wall set ends). (00:16:00)
The One With The Red Sweater - S8-E2
Continuity mistake: Monica is sitting in the living room with all her wedding presents, waiting for Chandler to return. She begins to open a large parcel and reveals a brown cardboard box. Then the camera moves to Joey, and when it moves back, the parcel is wrapped up again. This happens about three times. (00:05:05)
The One With The Apothecary Table - S6-E11
Visible crew/equipment: After Janine tells Joey that she'll apologize to Monica, in the shot of Janine walking into the hallway the end of the hall's set wall can be seen at the left side of the screen, and the corner of the camera can be seen moving at the right side of the screen.
The One With Joey's New Brain - S7-E15
Character mistake: After Susan Sarandon slaps Joey the first time, after he tells her that her character is dying on DOOL, she turns away and right before she is off camera she smiles, instead of maintaining her anger. (00:06:05)
The One With the Sharks - S9-E4
Revealing mistake: While Monica and Rachel are talking about Chandler's "jollies to Jaws" Rachel's wearing a colorful flowery top, and after Joey walks in just as Monica takes her seat at the table in the closeup, it's Jennifer Aniston's stand-in, wearing a blue top, who is seated beside Monica. Rachel's hair is wavy in the flowered top, but straight in the blue top (viewed in widescreen). (00:12:22)
Revealing mistake: In the episode where Joey is doubling Al Pacino's butt you can clearly see his shadow when he's shooting the scene in the shower, and he's wearing boxer shorts. (00:13:20)
Continuity mistake: The number of the flats near the start of the first series was 4 and 5. After a few shows they changed to 19 and 20. [The producers realised that the numbers 4 and 5 were for apartments on the lower floors and had shown Monica's apartment to be much higher up so they changed the numbers - it's still a mistake but there's the reason.]
The One With Phoebe's Ex-Partner - S3-E14
Visible crew/equipment: When Phoebe and Leslie finish singing the song Sticky Shoes, as they're hugging each other in the side shot, the second camera can be seen at the left side of the screen. (00:13:00)
The One With Phoebe's Ex-Partner - S3-E14
Visible crew/equipment: After Ross finds out that Mark quit his job, when Rachel and Ross leave the office, the second camera can be seen as the shot pans to the right, at the right side of the screen. (00:06:15)
The One With The Worst Best Man Ever - S4-E22
Visible crew/equipment: While Joey, Ross, and Chandler are waiting at the vet's office, in the following flashback scenes with the duck, when Joey bathes the duck the end of the bathroom set wall can be seen at the right; and when Chandler's sitting in the canoe with the duck in the pail, a crewmember can be seen where the set wall ends. (00:19:45)
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 Chandler In A Box - S4-E8
Visible crew/equipment: After Kathy tells Chandler goodbye and leaves Joey lifts the lid from the box, and when Chandler stands up in the box we can see the end of the living room set wall and the pink set wall.
The One With The Princess Leia Fantasy - S3-E1
Visible crew/equipment: After Phoebe's Princess Leia impersonation in front of Ross it cuts to Joey watching Wheel of Fortune, and in the next shot as Chandler walks in the camera can be seen at the right side of the screen.
The One With Rachel's Date - S8-E5
Visible crew/equipment: While Phoebe and Tim are at Central Perk, when Tim's beeper goes off he blows Phoebe a kiss when he leaves, and as Phoebe catches that kiss and throws it away have a look at the left side of the screen, where the Central Perk wall ends we can see part of Monica's restaurant kitchen set - the door and the wall beside it. (Widescreen version).
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.