The One With The Cake - S10-E4
Visible crew/equipment: After Joey describes Emma's funny Elmo cup to Phoebe, it cuts to Monica and Chandler walking in, and to the right of the door we can see the bulletin board is cut in size partially covering the hole in the wall. Later, when Phoebe and Joey leave after the wind-up toy race not only is this visible again, but through the hole we can see the other hole in Monica and Chandler's wall.
The One With The Cake - S10-E4
Visible crew/equipment: When Monica is talking to Chandler about waking Emma up, as she walks over to him, crew lights are visible in the top left corner of the screen. (00:05:35)
The One With The Cake - S10-E4
Revealing mistake: When Rachel and Ross are on the way back, if you look at Ross you can see a purple tinge to the side of his face. This is from projecting the background. (00:17:30)
The One With The Cake - S10-E4
Plot hole: Judy says that both her parents died very young. However, we saw her mother's death in "The One Where Nana Dies Twice" and she was quite old. Also, in Season 7, 'TOW Phoebe's cookies', Jack Geller tells Chandler that his father in law still thinks he is a lawyer and says "So if you ever see me giving them legal advice, just nod along," implying that Judy's parents were both still alive.
The One With The Cake - S10-E4
Visible crew/equipment: After Rachel announces that Phoebe and Joey will perform something, Phoebe asks Joey if he'll be nervous because he has nothing prepared, and when Joey replies that he does it every day with three cameras pointed at him, it's perfect timing that in the next shot we can see filming equipment at the right side of the screen.
The One With The Cake - S10-E4
Visible crew/equipment: At Emma's birthday party, Joey and Phoebe are discussing the performances they are doing for Emma. The balloons placed behind them reflect the stage and spot lights. This happens throughout the episode in most of the balloons.
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: 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: 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 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
Audio problem: When Chandler says, "Ironically, that was the Maxim thing", you can tell it's an overdub. The volume and the background noise is different, and we don't see a shot of him speaking these words. (00:11:20)
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)
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.