The One Where Ross Dates a Student - S6-E18
Continuity mistake: When Chandler, Joey and Ross are talking about Donna Keystone from college, Ross is holding a water bottle; it disappears, then he is holding it again. (00:13:15)
The One Where Ross Dates a Student - S6-E18
Continuity mistake: In the dinner scene between Chandler and the girl from college, the spoon in front of Chandler moves without him touching it. (00:13:45)

The One Where Ross Dates a Student - S6-E18
Continuity mistake: When Rachel and Joey are at Joey's apartment throwing wet paper towels at the entertainment unit, Phoebe comes in to ask Rachel to switch back to Monica's apartment. During the scene, Phoebe is standing in front of the entertainment unit, and the wet paper towels' number and positions change between shots. (00:18:10)
The One With Joey's Fridge - S6-E19
Continuity mistake: The handle to the fridge door is on the left, so when it opens the inside is visible. In earlier episodes the handle was on the right and it opened out towards the room, blocking the inside from view. (00:00:05)

The One With Joey's Fridge - S6-E19
Continuity mistake: When Joey pushes Ross against the fridge, a box falls from the top of the fridge onto the shelf beside it. A few seconds later when Joey turns to Chandler, we can see over his shoulder that the box is back on the fridge. (00:08:55)
The One With Mac & C.H.E.E.S.E. - S6-E20
Continuity mistake: When Chandler answers Joey's phone there is a drawing on the magnadoodle. However in the next shot it has vanished with no time. (00:17:20)

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 With Mac & C.H.E.E.S.E. - S6-E20
Continuity mistake: In the episode before, Rachel's hair is just underneath her shoulders. Then, a few weeks later when Ross gets back from Spring Break, it's a lot longer than before.
The One With Mac & C.H.E.E.S.E. - S6-E20
Continuity mistake: As Chandler is writing on the board to remind himself about Joey's audition, the door opens as he's writing "Joey", and there are a bunch of squiggly lines under the y. As Chandler is thinking back at that moment and it moves to present tense, he looks over to the board, and the squiggly lines are different.

The One Where Ross Meets Elizabeth's Dad - S6-E21
Continuity mistake: When Chandler is about to put the toilet paper on the table, the picture with the little girl is facing Phoebe. In the next shot, the picture is facing Chandler. Two shots later, it's facing Phoebe again, and then Chandler again in the next shot. (00:08:15)
The One Where Ross Meets Elizabeth's Dad - S6-E21
Continuity mistake: When Monica and Chandler enter the apartment arguing about what time they were supposed to meet, Monica has her handbag strap over her right shoulder, and then takes it off. When the shot switches to Phoebe claiming to know what time they said they would meet, the handbag strap is back over Monica's right shoulder, and then she takes it off again. (00:16:40)

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 Where Paul's The Man - S6-E22
Continuity mistake: When Monica is listening to the answering machine, the bread in the blue and white bag behind her changes position. (00:12:40)
The One Where Paul's The Man - S6-E22
Continuity mistake: When we hear the recording of Chandler answering the phone, it sounds nothing like what Chandler actually said. (00:13:00)
The One Where Paul's The Man - S6-E22
Continuity mistake: When Monica is blaming Phoebe for Chandler hearing the wedding message, Phoebe puts the magazine down on her lap and it's closed, but in the next shot it's open. (00:15:40)
The One Where Paul's The Man - S6-E22
Continuity mistake: In the opening scene in Central Perk when Paul (Elizabeth's dad) takes Ross to one side to talk to him you can see the girl in the blue top enters the door twice: first the shot after Paul says "I'm funny like that" and then again after Ross says "I realise it upsets you".
The One With The Ring - S6-E23
Continuity mistake: When Rachel is talking to Monica about Paul crying, just before Rachel leaves, Monica has her hair over her left shoulder; the shot cuts and she now has most of her hair over her right shoulder. (00:09:50)
The One With The Ring - S6-E23
Continuity mistake: Paul finally opens up, and cries like a baby to Rachel. While talking to her at the breakfast bar in the kitchen (when Rachel is trying to distract him with sex), he's wearing a white linen shirt that constantly changes between tear-stained and wrinkled to ironed and clean. (00:14:35)
The One With The Proposal, part 1 - S6-E24
Continuity mistake: When they are in Central Perk deciding who will go with Rachel to the auction, Rachel's purse and the cups in front of Joey move around. (00:02:20)
The One With The Proposal, part 1 - S6-E24
Continuity mistake: In the scene where Richard is being seated next to Chandler and Monica, the amount of champagne in Chandler's glass changes. (00:09:20)
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.