The One After Joey And Rachel Kiss - S10-E1
Revealing mistake: Just as they are getting ready to leave Barbados, Ross goes to speak to Chandler in the hotel room. The view outside the window is obviously a painting, or hanging. (00:10:55)
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 Where The Stripper Cries - S10-E11
Revealing mistake: When Monica collapses onto the beanbag chair at the very end of the episode, we can see the bottom of her fat suit below the hem of her skirt.
The One Where The Stripper Cries - S10-E11
Revealing mistake: During the 80s flashback, Monica and Rachel's cups are obviously empty.
The One With Phoebe's Wedding - S10-E12
Revealing mistake: Just before we see everyone setting the wedding up outside, there is a sweep shot of the city with snow falling. It's very obvious that this snow is added digitally and it's very badly done. There is no snow on any of the buildings, and there is no snow hitting the surface of the water. (00:20:50)
The One With Phoebe's Wedding - S10-E12
Revealing mistake: At the wedding, none of the snow melts when it has been sitting on people for several minutes. Occasionally when it gets brushed off clothes it just sticks to hands and sleeves, again for several minutes without melting. (00:21:15)
The One Where Estelle Dies - S10-E15
Revealing mistake: When Chandler and Monica are at the door of the house you can see that it is a fake background behind Chandler. (00:09:35)
The One With Rachel's Going Away Party - S10-E16
Revealing mistake: The twins are dolls. They don't move, and the way they are being carried indicates they don't weigh much.
Revealing mistake: When Chandler and Monica try to change the babies, Courteney Cox's pregnant belly is visible. (00:16:20)
Revealing mistake: When the first baby is born, Monica and Chandler are asked by the doctor if they would like to cut the umbilical cord. However, just before this line is delivered, the baby is moved and its navel is visible.
Revealing mistake: When Phoebe and Ross hit heads while in the cab on the bridge, they only just tap heads. Not enough to make them scream in pain. (00:05:15)
Revealing mistake: When everyone leaves the apartment together for the last time, they show Chandler and Monica with the twins in the stroller, and you can tell they are dolls.
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.