The One with the East German Laundry Detergent - S1-E5
Visible crew/equipment: When Rachel jumps into the cart, and the rude woman is bending over, you can see a mike pack underneath the back of her T-shirt. (00:21:30)
The One with the Dozen Lasagnas - S1-E12
Visible crew/equipment: When Ross is on the balcony trying to comfort Rachel after she has split up with Paolo, we see a couple of shots from the balcony looking into Monica's apartment. If you look at the top of the screen you can see where the walls of the set end, and all the stage lights hanging from the ceiling of the studio. (00:18:35)
The One with the Dozen Lasagnas - S1-E12
Visible crew/equipment: When Paulo says goodbye to Phoebe, a boom mic can be seen at the top of the screen bobbing in and out at the top of the pillar. (00:17:45)
The One with Two Parts: Part 1 - S1-E16
Visible crew/equipment: At the end of this episode when Rachel falls off the balcony, when we are looking out from Mr. Heckles' apartment, a boom mic is visible at the top of the screen just above him. (00:21:30)
The One with George Stephanopoulos - S1-E4
Visible crew/equipment: When Monica climbs out the window with the pitcher of Tiki Death Punch while Rachel and Phoebe are on the balcony, we can see the end of the set wall inside and a crew member moving around back there.
The One with the Ick Factor - S1-E22
Visible crew/equipment: After Ethan and Monica talk about "at gunpoint" being a place, when Monica asks Ethan to stay over it cuts to a shot facing Ethan and we can see that the back wall is less than half a wall.
The One with the Dozen Lasagnas - S1-E12
Visible crew/equipment: When Chandler and Joey are talking about buying a table, a line of stage lights is visible in the tv. (00:07:25)
The One with Two Parts: Part 1 - S1-E16
Visible crew/equipment: When Rachel is taking the Christmas lights down, a boom mic is visible as the camera pans down when we first see her. (00:21:15)
The One Where Underdog Gets Away - S1-E9
Visible crew/equipment: When Monica shuts the TV off while watching skiing, there is a closeup of the screen as it goes blank. You can see reflected in the blank screen an image of a man in a long sleeved shirt and tie, who does not correspond to any of the characters in the room. (00:08:00)
The One with Two Parts: Part 1 - S1-E16
Visible crew/equipment: At the Lamaze class just before Ross and Susan argue about who should lie on the floor, a boom mic can be seen in the top left corner of the screen. (00:08:50)
The One with Two Parts: Part 1 - S1-E16
Visible crew/equipment: Just after the credits, before we see a close up of Ross, a boom mic appears at the top of the screen in the centre of the window on the right. (00:01:30)
The One with the Ick Factor - S1-E22
Visible crew/equipment: When Rachel is telling everybody about the dream she had with her, Chandler and Joey in it, Ross stands up and starts talking. When he does, the stage lights are visible in the TV. (00:13:40)
The One with Two Parts: Part 1 - S1-E16
Visible crew/equipment: In Central Perk when Ross realises he's going to be a father, a black and white boom mic can be seen at the top of the screen. (00:16:50)
The One with the Fake Monica - S1-E21
Visible crew/equipment: After Marcel has humped the chair, when it cuts to Joey walking in saying that there already is a Joseph Stalin, we can see the reflection of a crewmember (presumably female) in the small mirror on the wall who's wearing a black top - and it's not Rachel, the angle is off.
The One with the Candy Hearts - S1-E14
Visible crew/equipment: Just as Joey and his date are leaving, a stage light and the top of the set drop into view above Chandler. (00:08:10)
The One with the East German Laundry Detergent - S1-E5
Visible crew/equipment: When the horrible woman enters, a tape marker is visible on the floor by the machines. (00:11:20)
The One Where Monica Gets a Roommate - S1-E1
Visible crew/equipment: We get a close-up of the coffee pot when Rachel asks if anyone would like some. In this shot, there are 3 stage lights reflected clear as day. (00:27:50)
The One Where Nana Dies Twice - S1-E8
Visible crew/equipment: When the scene cuts from Joey and Mr. Geller watching the game, to several people watching the game, a boom mic is visible at the top of the screen and the camera tilts slightly. (00:19:00)
The One Where Nana Dies Twice - S1-E8
Visible crew/equipment: When Monica and Ross meet up with their parents and their nana, a boom mic is visible at the top of the screen. (00:04:20)
The One Where Underdog Gets Away - S1-E9
Visible crew/equipment: When Chandler runs into the apartment to say Underdog has gotten away, a crew member can be seen reflected in the sun shaped mirror behind him walking through the back of the shot. It can't have been Rachel, Monica, Phoebe or Joey because Joey is sitting down and Rachel, Monica and Phoebe are nowhere near the mirror. (00:14:05)
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.