The One With Ross's Tan - S10-E3
Continuity mistake: Ross' tan keeps changing shades. It gets lighter then darker, then lighter again. (00:12:40)
The One With Ross's Tan - S10-E3
Continuity mistake: When Ross gets a spray on tan, there is one shot where he is being sprayed in the face. Instant camera cut then it's on his chest, not near his face. (00:19:35)
The One With Ross's Tan - S10-E3
Continuity mistake: Chandler walks away from Ross's apartment at the end. But he walks to where the kitchen should be. (00:21:15)

The One With Ross's Tan - S10-E3
Continuity mistake: In the scene where Joey and Rachel are sitting on the couch in their apartment after they decide their relationship is hopeless Rachel puts her head on Joey's shoulder. Her hair is on her face but when she lifts her head up in the very next shot her hair is now behind her right ear which she couldn't have done because her hands never left her lap. (00:22:00)

The One With The Cake - S10-E4
Continuity mistake: When Monica's mum and dad are leaving the party, they are standing next to each other while her dad explains why he can not drive anymore. Her mum has both hands in front of her holding on to her purse, in the next shot one arm is around Monica. (00:13:50)

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 Cake - S10-E4
Continuity mistake: Phoebe's robot in the toy race is behind Joey's. Joey then says unlucky and picks his toy up. Phoebe then picks hers up and it is about a metre in front of Joey's. The toy can't move that fast. (00:16:40)

The One With The Cake - S10-E4
Continuity mistake: When Ross and Rachel are driving back, Ross starts to put the seatbelt on. Instant cut, and he has his seatbelt on. (00:17:35)

The One With The Cake - S10-E4
Continuity mistake: Just before Rachel and Ross come back from the cake store, Monica is holding Emma on her lap. Emma is holding a green toy in one shot, when the camera angle changes it is nowhere to be seen. (00:19:30)
The One With The Cake - S10-E4
Continuity mistake: Near the end, Monica rearranges Emma's stuffed toys in order of size. When you next see them they are jumbled up, then later they return to being neatly lined up again. (00:19:40)

The One With The Cake - S10-E4
Continuity mistake: At the end after Rachel and Ross have come back from the cake store, when they are asking Emma how old she is, we can see Joey walking to sit down, then in the next shot he is sat down, then walking to sit down again. (00:20:25)
The One Where Rachel's Sister Babysits - S10-E5
Continuity mistake: Rachel and her sister are in Rachel's room. When Rachel picks up Emma, Emma has nothing in her arms, but in the next shot when Rachel is holding her, she has a toy in her arms though she had no time to get one.
The One Where Rachel's Sister Babysits - S10-E5
Continuity mistake: While everyone is booing Mike and Phoebe, the guy sitting behind Phoebe changes position in every shot.
The One Where Rachel's Sister Babysits - S10-E5
Continuity mistake: When Ross is looking at Emma in the coffee house he turns and looks at the guys on the couch and mouths the word "what." Then in the next shot he does it again.
The One With Ross's Grant - S10-E6
Continuity mistake: When Monica comes round to Phoebe's, Phoebe reminds her that she's got to clear out stuff. In this wide shot Monica has both hands by her sides, but when it cuts to her finishing saying "oh right", her right hand is now gripping her bag's strap. (00:05:00)

The One With Ross's Grant - S10-E6
Continuity mistake: When Aisha Tyler and Greg Kinnear put one hand on Ross's face, they bring those hands together and they interlock fingers, then the camera changes positions and they interlock fingers again. (00:22:20)
The One With Ross's Grant - S10-E6
Continuity mistake: When Charlie and Benjamin are at the restaurant, Benjamin says "I can't believe you chose this restaurant. You remember that night?" To which Charlie replies "I can't believe they let us back in here." However in "The One With The Fertility Test" Charlie has never been to New York before.
The One With Ross's Grant - S10-E6
Continuity mistake: After Joey puts the video in the player, it's clear the video doesn't go all the way in, and even starts to eject itself. The shot cuts, and without him making any moves to replace the tape, it plays fine.
The One With Ross's Grant - S10-E6
Continuity mistake: When Phoebe tells Rachel and Monica that Mike lets her keep her box of hair, Rachel's chopsticks are down, by the plate. In the next shot, she's holding them close to her mouth.
The One With The Home Study - S10-E7
Continuity mistake: When Phoebe and Mike first donate the money to the children, the way the man is holding the cheque changes depending on the shot. (00:03:15)
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.