The One with Mrs. Bing - S1-E11
Revealing mistake: When Chandler finds out Ross kissed his mom, he leaves and slams the door behind him. After he slams the door, the wall wobbles slightly, revealing it's part of the set. (00:15:05)
The One with Mrs. Bing - S1-E11
Continuity mistake: The position of Mrs. Bing in relation to the pay phone keeps changing during her conversation with Ross at the restaurant. (00:08:55)
The One with Two Parts: Part 2 - S1-E17
Other mistake: Rachel is limping in the hospital for the first time. When she gets back home, she walks perfectly fine. Then in the hospital, she starts to limp again.
The One With Princess Consuela - S10-E14
Continuity mistake: When Ross hugs Rachel in Central Perk, after finding out she has been fired, he leans his face against hers twice.
The One With Ross's Library Book - S7-E7
Continuity mistake: When Phoebe is eating the muffin, it has no white paste on it. Then the shot changes and there's a line of white paste.
The One With Ross's Library Book - S7-E7
Continuity mistake: After Monica tells Chandler that they are going to have lunch with Janice, it shows Central Perk. The people in the window are different when the shot changes.
The One With Ross's Library Book - S7-E7
Continuity mistake: When Rachel asks Ross what's wrong, her hand is up. Shot changes and it's down.
The One With Ross's Library Book - S7-E7
Continuity mistake: When Janice sees Monica's ring, she's wiping her hands with a rag, then it disappears. (00:03:50)
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).
Visible crew/equipment: When Ross and Rachel realise they are in an empty apartment, studio lighting can be seen over their heads in the ceiling as Ross leads Rachel into the centre of the room. (00:04:35)
The One Where Chandler Doesn't Like Dogs - S7-E8
Visible crew/equipment: When Chandler sees the empty dog basket on the floor at Ross' there is a panning shot to the door. If you look carefully, you can see a crewmember wearing blue jeans and white shoes. (00:17:25)
The One With The Cake - S10-E4
Continuity mistake: When Jack and Judy leave Joey's apartment, there is a birthday banner on the counter that has fallen off. When Monica, Chandler, Joey and Phoebe are racing the toys to see who gets to go, the banner is back on. In this time no-one has fixed the banner as there is not enough time for them to do so off camera and the people on camera don't fix it. It's most clear that it's back on when Monica is saying, "Technically, our dog never crossed the finish line". (00:14:05 - 00:17:05)
The One with the Monkey - S1-E10
Visible crew/equipment: After Max tells Phoebe that he and David got the grant and are leaving for Minsk on January 1st, when Phoebe goes to see David, just as she knocks on the door a boom mic can be seen moving at the top of the screen, before it cuts to David's closeup. (00:12:15)
The One Without The Ski Trip - S3-E17
Continuity mistake: When Phoebe is saying how she gets out of tickets, she is pointing at herself in one shot and not in the very next shot. (00:05:50)
The One With The Football - S3-E9
Continuity mistake: At the end, Chandler points at Joey, and when he does so, his sleeve goes from rolled down to rolled up instantly. (00:22:10)
The One With The Football - S3-E9
Visible crew/equipment: Just before Monica tackles Chandler to the floor, there is a shot with a very large boom mic visible at the top of the screen (only visible in fullscreen version). (00:13:10)
The One With The Football - S3-E9
Continuity mistake: Chandler says he's been preparing for something his whole life. When he says this, his right sleeve is rolled up. Camera changes, and now it's rolled down. (00:10:40)
The One With The Football - S3-E9
Continuity mistake: When Joey tells Chandler to prepare to feel very bad about himself, he has the football in his right hand. When the shot changes, it's in his left. (00:10:30)
The One With The Football - S3-E9
Continuity mistake: When Joey introduces himself to the Dutch lady, the way and where he holds the football changes between successive shots. (00:08:40)
The One With The Football - S3-E9
Continuity mistake: When Rachel asks Ross if not catching Joey was part of his football strategy, she has her hands outstretched in one shot and then on Ross' shoulder in the next. (00:07:10)
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.