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)
The One That Could Have Been, part 2 - S6-E16
Continuity mistake: Rachel is talking to Joey in his apartment after waking up the next morning, looking messy and rumpled. As she talks, her bra strap slips down her arm. In one shot (as she says "I'm a horrible person"), the strap is all the way down her arm and then in the next shot it is tucked under her shirt. (00:10:00)
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 Chandler Can't Cry - S6-E14
Continuity mistake: When they're watching the vampire video, Monica, Chandler, and Rachel are sitting on the couch, but in the closeups of the TV we can see the couch in the reflection and it's empty.
Continuity mistake: Just before Chandler gives Monica the mixed tape, he tries to manipulate a coat hanger into something feasible. He stretches it out and holds it up, saying "Yes, honey, I made it myself," then the camera cuts to another angle as he throws it down. After the cut the hanger is not as stretched as it was before. (00:10:40)
Continuity mistake: Joey's Hand moves from putting it to his mouth to the plate instantly at breakfast. (00:06:35)
The One With The Apothecary Table - S6-E11
Continuity mistake: In the previous episode, Monica's Christmas tree is up in her apartment. After the party, Joey kisses Janine. In the next episode, he walks into Monica's apartment and says he just kissed her. However, Monica's tree is down and they have all changed their clothes. Surely if he just kissed her then it is still the same night of the party, therefore the tree should be up and Monica, Ross and Joey should be wearing the same clothes from the party. (00:00:05)
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: In the previous episode Monica had a very bad cold. This episode carries on immediately after the end of the last one (Monica's still in her dressing gown from earlier), but Monica isn't coughing or sneezing at all anymore. (00:00:05)
The One That Could Have Been, part 1 - S6-E15
Continuity mistake: In the scene where Joey gives Chandler the orange juice and says sorry, the paper cup's logo faces Joey's hand, then the shot goes to Chandler and when it comes back, the logo on the cup faces Chandler. (00:15:15)
Continuity mistake: In the previous episode, Ross rings the helpline of the makers of the pen and is told the pen won't come off. Yet in this episode it vanishes from Ross and Rachel's faces between getting up and going to breakfast. (00:02:25)
The One With The Proposal, part 2 - S6-E25
Continuity mistake: When Monica is in Richard's apartment she gets all worked up, so Richard gives her a hug to calm her down. She goes into the hug with her arms curled up in front of her face, but when the camera angle changes, they are at Richard's back. (00:13:50)
The One Where Ross Dates a Student - S6-E18
Continuity mistake: The fireman's helmet alternates being under each arm between shots. (00:05:10)
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 With Ross's Teeth - S6-E8
Continuity mistake: In the opening coffee house scene Ross is holding a red folder, then it disappears and then he has it again. (00:02:05)
The One That Could Have Been, part 2 - S6-E16
Continuity mistake: When Phoebe is in the hospital bed and Monica gives her a cup of herbal tea, Phoebe is shouting at her for putting honey in it. As the shot changes back and forth the spoon in the cup changes position. (00:02:00)
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)
Continuity mistake: When Ross and Rachel are in bed, and Rachel says she remembers laughing a lot, and Ross says "Then we didn't have sex," Rachel turns her head away from Ross twice. (00:03:10)
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 Chandler Can't Cry - S6-E14
Continuity mistake: In this episode Chandler says he can't cry, but in series 4 when he broke up with Kathy he was seen crying, and other times - it's just this episode it's apparently an issue.
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.