The One With Ross' New Girlfriend - S2-E1
Visible crew/equipment: When Rachel's at the airport and freaks out after seeing Ross with Julie, right before she steps up on the chair the grey crash mat can be seen on the floor, behind the man who's wearing white pants and is seated.
The One With Ross' New Girlfriend - S2-E1
Continuity mistake: At the beginning when Rachel falls and starts bleeding, you can see that the wound is somewhere up above her forehead because the blood is running from the wound up there. However, throughout the rest of the episode she has a bandaid going horizontally across her forehead, nowhere near where the apparent wound was. (00:01:20)
The One With Ross' New Girlfriend - S2-E1
Deliberate mistake: The door to Monica's bedroom is open in many shots, such as when Ross introduces Julie, and we can see that there's a wall (with a framed picture) directly opposite the doorway, but when Phoebe's giving Monica the haircut they're in Monica's bedroom and there's no such wall in front of the door.
The One With Ross' New Girlfriend - S2-E1
Continuity mistake: When Paulo comes out of Rachel's bedroom to greet the group, the robe he is wearing is obviously untied and hanging open. After we see how everyone reacted to him being there, we again see Paulo but now the robe is securely tied even though neither he nor Rachel changed positions between shots. (00:11:10)
The One With Ross' New Girlfriend - S2-E1
Continuity mistake: At the very beginning of the episode, the blood on Rachel's head changes a few times throughout that opening scene. (00:01:15)
The One With Ross' New Girlfriend - S2-E1
Other mistake: After Rachel takes the phone from Ross and hangs up on Julie, when she's sitting at the table there's a bottle of Evian water in front of Monica with part of its brand name covered - the letters "e" and "n" are whited out leaving "via" on the bottle.
The One With Ross' New Girlfriend - S2-E1
Continuity mistake: When Chandler has just got back from seeing Joey's 'bad' tailor, Joey says, "That's how they do pants". Chandler turns to look at him twice. (00:17:30)
The One With Ross' New Girlfriend - S2-E1
Revealing mistake: At the end, when Rachel and Ross are talking on Monica and Rachel's balcony, the edge of the "brick" wall behind them has a gap in it. The facade is obviously a thin plastic sheet made to look like bricks and mortar, and it has pulled away from the surface it is attached to.
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.