Continuity mistake: When Rachel and Monica knock on Danny's door and he opens it, there is a wall a few feet behind him. Later, when Rachel shows up at Danny's apartment to cancel their date, she enters into an open room and there is no longer a wall in front of the door. Danny's apartment is supposed to be one floor directly below Chandler and Joey's apartment. This was obviously the same set for their apartment that was used for Danny's and the wall was added for that shot to disguise it.
The One With The Inappropriate Sister - S5-E10
Continuity mistake: When Rachel and Monica are arguing about her meddling, Monica raises her hand to her face and you see a sparkly engagement ring on her finger. Her character wasn't engaged but Courteney Cox was at the time. (00:07:05)
The One With Rachel's Inadvertent Kiss - S5-E17
Continuity mistake: When Rachel returns from her first interview at Ralph Lauren she takes out a bottle of water out of the fridge. In the following shot her hands are empty and there are only Chandler's and Joey's bottles on the table. Rachel's bottle reappears on the table next to Chandler's and Joey's bottles (that are also standing closer together than before) for a moment just when Chandler starts saying "Well, you could have tried not kissing him" and then vanishes again. (00:06:20 - 00:07:15)
Continuity mistake: Joey's bedroom door opens and closes as the camera goes between him and Monica and Chandler when he is telling him he doesn't want to see them kissing.
The One With Rachel's Inadvertent Kiss - S5-E17
Continuity mistake: Joey is watching Ross from Monica's window and goes searching for the hot girl. The exterior shot crossing the street between buildings is inconsistent with the interior shots, which show them looking at each other across an alley with no visible fire escapes. The exterior shot crosses a street to a building with street-facing fire escapes on every apartment.
The One With The Inappropriate Sister - S5-E10
Continuity mistake: When Joey and Phoebe are talking to each other on the couch, Rachel tucks her hair behind her ears, but in the next shot it's moved.
The One With The Inappropriate Sister - S5-E10
Continuity mistake: When Joey is talking to Ross about him being an actor, the shot changes and Ross is holding his beer in a different position.
The One With The Inappropriate Sister - S5-E10
Continuity mistake: When Rachel and Monica are talking about Danny and the girl on the subway, Rachel has tiny bits of her fringe hanging out and it moves between shots without any movement.
The One In Vegas, Part 2 - S5-E24
Continuity mistake: When Monica and Chandler kiss under the table, as "Everybody Loves Somebody" plays, Monica is shown smiling. She then closes her mouth. In the next shot, she is smiling again without any time to do so.
The One With All The Resolutions - S5-E11
Continuity mistake: Immediately when the opening scene starts, we hear from the crowd on the television that there is less than 60 seconds to midnight. However, 60 seconds later in the scene, the countdown still hasn't reached zero.
The One With The Ball - S5-E21
Continuity mistake: When Rachel is outside the coffee shop trying to sell the cat, in between shots, it goes from a standing to sitting position multiple times.
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.