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 Cake - S10-E4
Visible crew/equipment: After Joey describes Emma's funny Elmo cup to Phoebe, it cuts to Monica and Chandler walking in, and to the right of the door we can see the bulletin board is cut in size partially covering the hole in the wall. Later, when Phoebe and Joey leave after the wind-up toy race not only is this visible again, but through the hole we can see the other hole in Monica and Chandler's wall.
The One With Ross's Tan - S10-E3
Visible crew/equipment: After Monica gets the call from Chandler about the fake car accident and leaves Phoebe with Amanda, in the next shot of Joey walking into his apartment the bulletin board that usually hangs beside the door is cut to about a quarter of its size, and it's covering part of the hole in the wall.
The One Where Monica Gets a Roommate - S1-E1
Continuity mistake: At the end of the episode when Ross picks up his jacket, there is a blue bowl on the small table by the pillar and nothing on the main kitchen table. In the next shot, the blue bowl has moved to the large table. (00:27:10)
The One With The Boob Job - S9-E16
Revealing mistake: When Phoebe and Mike walk into Central Perk and announce they're moving in together, Chandler, Monica, and Ross, who's wearing a sweatshirt and khakis, are all sitting on the couch, and after Phoebe's comment about loading up the Volvo and wanting to be a soccer mom, it's David Schwimmer's stand-in, wearing a blue button-down shirt and jeans, who is seated beside Chandler.
The One Where Monica Gets a Roommate - S1-E1
Continuity mistake: The door to Monica's bedroom is shown open, then closed, then open, and then closed during the scene in which Paul arrives for their date. (00:09:00)
The One Where Monica Gets a Roommate - S1-E1
Continuity mistake: In the scene where the friends scoot the table over to see Monica's date with "Paul the wine guy", the cup in front of Chandler changes position. (00:18:55)
The One With Joey's Porsche - S6-E5
Other mistake: Immediately after Joey walks in as Chandler is handling the baby, we see him staring and waving in a direction past the stage. (00:06:55)
The One With Ross's Denial - S6-E3
Visible crew/equipment: After Ross tells Rachel about Warren's apartment he gives her Warren's phone number, and in the closeup while Rachel hugs Ross, and also in the following wideshots which face Ross the camera can be seen at the right side of the screen.
The One With Monica and Chandler's Wedding, Part 2 - S7-E24
Revealing mistake: At the point in the ceremony where Joey forgets the rings, the camera pans out and you see Chandler step sidewards to get the ring from Ross, and Monica step sidewards to get the ring from Rachel and Phoebe. As Monica moves, her dress slides across and one of her feet is revealed; it has what looks like a brown boot or heavy brown shoe on it. (00:20:05)
The One With The Stain - S8-E7
Visible crew/equipment: When Brenda is cleaning the top of the cabinets, stage lights can be seen on the top right-hand corner of the screen. (00:11:45)
The One With Chandler In A Box - S4-E8
Visible crew/equipment: When Kathy walks in while Chandler's in the box, after Phoebe tells her, "He can't talk right now," in the shot facing Kathy the end of the set wall can be seen, and there's a plastic cup with a straw sitting on a shelf off stage.
The One With The Apothecary Table - S6-E11
Visible crew/equipment: When Phoebe and Rachel stop in front of the Pottery Barn window, in the first shot facing them from inside the store window the end of the brick set wall can be seen, with the camera beside it, and can also be seen when Phoebe comments that it's their exact living room.
The One In Barbados, part 2 - S9-E24
Visible crew/equipment: While Joey's wearing the snorkel gear he blows a grape out of his snorkel tube, and when Charlie walks into the room the opening in the wall can be seen beside the door.
The One With The Mugging - S9-E15
Visible crew/equipment: When Ross walks into Central Perk and Phoebe asks him about his class before she tells him the truth, in the closeup of Ross the camera can be seen at the right side of the screen.
The One With Rachel's Other Sister - S9-E8
Visible crew/equipment: When Monica heads to Joey's apartment to get the pies Joey tells her it's just one pie now, and after Monica's comment about losing the will to scold we can see the hole in the wall beside the front door.
The One With Rachel's Other Sister - S9-E8
Visible crew/equipment: When Monica tells Joey that he has a red plate instead of a fancy plate because it's a game, just as Joey says that he can't believe he won, we can see the camera at the right side of the screen.
The One With Ross's Inappropriate Song - S9-E7
Visible crew/equipment: While Chandler and Joey are watching Richard's videotape, when Chandler's relieved it's just football he heads off to get beer, and in the next shot as he hears the sound of moaning we can see the opening in the wall behind the TV.
The One With Ross's Inappropriate Song - S9-E7
Visible crew/equipment: When Joey jumps on Chandler to shield him from seeing Monica's sex tape, the mat they land on is visible prior to the scene.
The One with All the Poker - S1-E18
Continuity mistake: When Chandler and Ross are explaining how Joey cried during their poker game, Joey's coffee mug is blue when he's holding it at the counter, but when Joey walks away from the counter his mug is yellow.
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.