The One With Rachel's Sister - S6-E13
Visible crew/equipment: After Jill comes to Monica's apartment, they are all around the table in the living room. As the camera is moving from Jill, to Monica and Chandler, who are sitting on the couch, a camera-man is visible in the kitchen behind them, complete with camera and trailing wires. (00:04:15)
The One Where Chandler Can't Cry - S6-E14
Visible crew/equipment: While Rachel's looking out Monica and Chandler's window she tells Joey that Ross is on a date with her sister, and just as Joey comments, "I didn't know we could date your sister," a crew member can be seen moving around near the front door at the left side of the screen, and we know it's not Chandler or Monica since they're still in the bedroom wearing robes in the next shot.
Visible crew/equipment: When Chandler points out to Joey that his oblivious comment was made in front of Ross it cuts to a closeup of Ross, and camera equipment can be seen at the right side of the screen, and it's still there in the next two closeups of Ross.
The One Where Ross Dates a Student - S6-E18
Visible crew/equipment: When Joey walks into Chandler's apartment, Chandler is sitting on the couch talking on the phone. Two microphones are visible. (00:06:20)
The One Where Ross Dates a Student - S6-E18
Visible crew/equipment: Just after Ross' girlfriend leaves the Central Perk, Ross walks towards the couch. Just before Rachel starts talking, the stage lights can be seen reflected in the glass above the entrance. (00:17:00)
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 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 With Joey's Fridge - S6-E19
Visible crew/equipment: In the scene where Rachel introduces Sebatian to Chandler, Monica and Phoebe, there is a visible boom mic at the top of the screen in the wide shot, right after Chandler says, "Turns out he is kinda funny".
The One With Mac & C.H.E.E.S.E. - S6-E20
Visible crew/equipment: A stage light can be seen at the top left hand side of the screen just after Joey slams the door shut after practising a scene with Phoebe. It is visible in front of the blue picture on the wall.
The One Where Paul's The Man - S6-E22
Visible crew/equipment: In the scene where Rachel is trying to hide Ross from Paul, when he's about to go into Paul's bedroom after he says "Did you really hear a bear?", look at the window behind Rachel when the shot is on her. You can see a large light reflected in the glass and it moves slightly (not just in conjunction with the camera, it moves before the camera shifts).
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 The Proposal, part 1 - S6-E24
Visible crew/equipment: After Ross breaks up with Elizabeth, when she throws the water balloons at him and he starts walking away, a crew member's feet are seen standing on a windowsill behind Ross. Additionally, when Ross has exited the building, just as Elizabeth calls to him and he turns around we can see a crewmember, presumably standing beside the second camera, at the bottom left corner of the screen. We know it's not a passerby because he is as tall as the second story window behind him, which means he's elevated on a platform or ladder. (00:19:15)
The One With The Proposal, part 1 - S6-E24
Visible crew/equipment: After Chandler tells Monica about the interesting website and fakes his opinion of marriage, right after Monica says, "Well, that's good to know," in the next wideshot the camera can be seen at the right side of the screen. (00:20:15)
The One With The Proposal, part 2 - S6-E25
Visible crew/equipment: When Chandler walks in and sees Monica, the boom mic is visible above Monica's head. (00:17:45)
The One With The Proposal, part 2 - S6-E25
Visible crew/equipment: After Joey fibs and tells Chandler that Monica went to her parents, when Chandler and Joey walk into the apartment, in the shot facing the hallway we can see some of the camera equipment past the doorway, and in the next wideshot of the apartment as the camera pans to Monica the overhead studio lighting rigs can be seen at the top of the screen.
The One With Monica's Thunder - S7-E1
Visible crew/equipment: After Ross walks in with the champagne and candy bar, in the shot of Monica shouting, "I'm getting married...," on the balcony, studio lighting can be seen inside above Joey.
The One With Monica's Thunder - S7-E1
Visible crew/equipment: When Monica says she's opened the door to the past, a little bit of a stage light is visible above her head.
The One With Phoebe's Cookies - S7-E3
Visible crew/equipment: When Chandler and Jack, both wearing robes, are walking toward the whirlpool room, just as Chandler tells Jack that he'd feel more comfortable if Jack didn't tell anyone what had happened, we can see the shadow of the boom mic moving across the wall at the right side of the screen.
The One With Phoebe's Cookies - S7-E3
Visible crew/equipment: When Ross asks what do with all the cookies, a boom mic can be seen at the top of the frame. (Full-screen version only).
The One With Rachel's Assistant - S7-E4
Visible crew/equipment: When Rachel holds up the Polaroid she took of her assistant, it appears to have been one of the actual photos taken in the earlier scene; you can see the edge of the set behind him, and the overhead lights in the black space to the right of the photo. (00:07:40)
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.