Continuity mistake: The number of the flats near the start of the first series was 4 and 5. After a few shows they changed to 19 and 20. [The producers realised that the numbers 4 and 5 were for apartments on the lower floors and had shown Monica's apartment to be much higher up so they changed the numbers - it's still a mistake but there's the reason.]
Continuity mistake: In the pilot episode, the guy Rachel left at the altar is called Barry Finkle. In all the other episodes his name is Barry Farber.
Continuity mistake: Mr Heckles's apartment number changes from 8 to 5.
The One Where Monica Gets a Roommate - S1-E1
Continuity mistake: When Phoebe cleanses Ross' aura, he holds up both hands to stop her. In the next shot his left hand is lowered. (00:02:50)
The One Where Monica Gets a Roommate - S1-E1
Continuity mistake: The door to Monica's bedroom is shown open, then closed, then open, and then closed during the scene in which Paul arrives for their date. (00:09:00)
The One Where Monica Gets a Roommate - S1-E1
Continuity mistake: When Monica asks Ross, 'Do you want me to stay?', her hands are in front of her, not touching Ross. In the next shot, her right hand is holding onto Ross's wrist. (00:09:10)
The One Where Monica Gets a Roommate - S1-E1
Continuity mistake: When Paul the Wine Guy first comes to Monica's apartment, Phoebe is standing in the kitchen telling Rachel that she just pulled out four eyelashes. But in the very next shot, you can see her sitting in an armchair in the living room. [Broadcast version only - in the extended DVD version there's a shot showing Phoebe walking to the chair.] (00:09:20)
The One Where Monica Gets a Roommate - S1-E1
Continuity mistake: When Ross shows Chandler and Joey the can of "Carol's favorite beer" it's unopened as Ross makes a crack about how he "should have known," but in the next shot we see Ross lifting the can and drinking from it, even though he never actually pulled open the stay-tab between the two shots (viewed in widescreen). [In the extended version of the episode you see Ross open the can before taking a drink. In the standard version, the mistake is valid]. (00:09:55)
The One Where Monica Gets a Roommate - S1-E1
Continuity mistake: When Ross, Chandler and Joey are setting up Ross' furniture and Ross is bent down saying, "And I cannot feel my legs," Ross is holding up a manual. When it cuts, the manual is suddenly lying on the floor. [In other versions, such as Netflix, the first shot shows the manual falling to the floor and the second shot does not exist. However, the mistake is valid for the TV broadcast version of the episode]. (00:11:45)
The One Where Monica Gets a Roommate - S1-E1
Continuity mistake: When Joey hides the bracket in the plant pot, the instruction sheet that is on the bookcase disappears instantly. (00:12:20)
The One Where Monica Gets a Roommate - S1-E1
Continuity mistake: The way Ross holds the can of beer changes between the full on shots and the shot of Chandler and Joey when just the can is visible on the side of the screen. (00:12:40)
The One Where Monica Gets a Roommate - S1-E1
Continuity mistake: While Joey and Chandler are at the apartment with Ross, a watch suddenly appears on Joey's wrist when he announces that he and Chandler are done with the bookcase, then the watch vanishes and reappears again in the following shots at the apartment. (00:15:40)
The One Where Monica Gets a Roommate - S1-E1
Continuity mistake: When Joey makes the joke about Ross being 8, Ross has his right left hand lowered. Camera changes to a different angle and it's raised, before switching back to the 1st angle and being lowered again. (00:15:50)
The One Where Monica Gets a Roommate - S1-E1
Continuity mistake: During Monica's date, she points her fingers and asks, "What were you going to say?" In the next shot she is gesturing with her hand. (00:16:00)
The One Where Monica Gets a Roommate - S1-E1
Continuity mistake: In the scene where the friends scoot the table over to see Monica's date with "Paul the wine guy", the cup in front of Chandler changes position. (00:18:55)
The One Where Monica Gets a Roommate - S1-E1
Continuity mistake: When Monica is saying bye to Paul, Paul goes to the screen left but the stairs are at the screen right. (00:19:20)
The One Where Monica Gets a Roommate - S1-E1
Continuity mistake: Near the end when Phoebe says to Monica, "C'mon give me your feet" she puts the red pen down on the blue paper. When Monica sits down though, the red pen is on the table and not the blue paper. (00:23:40)
The One Where Monica Gets a Roommate - S1-E1
Continuity mistake: Before Monica stomps on Paul's watch, the chair closest to the fridge does not have fabric backing, then when Ross eats the Oreo and walks toward his jacket the chair closest to the fridge is now fabric backed and his jacket hangs from a chair with no fabric, plus there are only four chairs around the table. However, when Ross picks up his jacket this chair is now fabric backed, the chair closest to the fridge doesn't have a fabric back yet again, and there are now five chairs around the table. (00:27:00)
The One Where Monica Gets a Roommate - S1-E1
Continuity mistake: At the end of the episode when Ross picks up his jacket, there is a blue bowl on the small table by the pillar and nothing on the main kitchen table. In the next shot, the blue bowl has moved to the large table. (00:27:10)
The One Where Monica Gets a Roommate - S1-E1
Continuity mistake: At the end of the episode, as a customer in Central Perk asks Rachel for more coffee, Chandler has set his cup of coffee on the table. In the next shot, he is holding it again. (00:28:05)
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.