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 crewmember'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 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 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 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 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 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 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 Where Ross Got High - S6-E9
Visible crew/equipment: After Ross and Monica blurt out each other's secrets to their parents, when Jack says, "And we kind of figured about the porch swing," in his closeup we can see the end of the set wall, with the soundstage behind it and many tape marks on the floor.
The One With The Routine - S6-E10
Visible crew/equipment: While Monica and Ross attempt to do the original end to their routine, instead of Monica catching Ross she jumps out of the way, and when Ross lands on the floor the corner of the crash mat can be seen. (Widescreen version).
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 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)
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 With Mac & C.H.E.E.S.E. - S6-E20
Continuity mistake: After Chandler has written the message on the Magna Doodle, the sliding eraser moves from the right to left side just as he leaves with Monica, and when Joey and Chandler are playing foosball, the barely legible "Joey" is now neatly written on the Magna Doodle, and its sliding eraser is again back to the right side.
The One Where Phoebe Runs - S6-E7
Visible crew/equipment: When Chandler is cleaning the apartment, you can see a camera on the right of the screen.
The One With Ross's Denial - S6-E3
Continuity mistake: When Monica and Chandler are eating, Monica's plate holds a sandwich and chips. When Joey comes in, Monica's plate contains no chips, and when he leaves the chips are back again. (00:04:00)
The One Where Chandler Can't Cry - S6-E14
Continuity mistake: When Chandler throws his copy of "Chicken Soup for the Soul" under the sofa and it goes across the floor to Monica's feet, she kneels down to pick it up by the counter next to the door, but when she rises, she's next to a chair that's under the table. (00:12:20)
The One Where Paul's The Man - S6-E22
Continuity mistake: When Rachel and Paul are on the couch at the cabin, the diet coke Rachel is holding switches (repeatedly throughout the scene) from her left hand to her right. (00:12:00)
The One With The Routine - S6-E10
Visible crew/equipment: Just as Phoebe walks into the apartment with the duck and chicken (to help find Monica's hidden presents), a crew member's leg/foot can be seen at the bottom left side of the screen.
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.