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.]
The One Where the Monkey Gets Away - S1-E19
Continuity mistake: While Rachel's babysitting Marcel she's watching the soap opera on TV, and when she points out Dr. Francis there's a closeup of the TV and when she points out Raven there's another closeup, but the TVs in both closeups are different, as well as the items that are near the TVs.
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: 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: 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 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: 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 with All the Poker - S1-E18
Continuity mistake: When Chandler and Ross are explaining how Joey cried during their poker game, Joey's coffee mug is blue when he's holding it at the counter, but when Joey walks away from the counter his mug is yellow.
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 with the Sonogram at the End - S1-E2
Continuity mistake: When Rachel loses the ring near the beginning, Chandler and Joey get off a chair to help look. But then the shot cuts to Monica, and behind her you can see Chandler at the fridge without enough time to get there. (00:05:40)
The One Where the Monkey Gets Away - S1-E19
Continuity mistake: After Marcel has escaped from the basement, he is eating a banana as a pair of arms reach out to grab him. These arms are supposed to belong to Mr Heckles, their weird neighbour, however the arms belong to someone young, large and hair free. (00:16:10)
The One with the Dozen Lasagnas - S1-E12
Continuity mistake: When Rachel is talking with Phoebe about Paolo,. she unrolls some kitchen paper and uses it as a tissue. Initially she's holding two torn halves attached to the roll, then when saying "He's a pig" it goes to a whole sheet not attached to any others, then when she sits down it's a whole sheet attached to the roll again. Plus when Phoebe sits too, in some shots the paper is on the table, in others it's not. (00:15:20)
The One with George Stephanopoulos - S1-E4
Continuity mistake: When Rachel gets her first paycheck, the envelope is already open, but she then rips it open. (00:04:20)
The One with the Boobies - S1-E13
Continuity mistake: We've seen the arrangement of Joey and Chandler's bathroom in two previous episodes (1x3, The One with the Thumb, and 1x12, The One with the Dozen Lasagnas) with the sink opposite the bathroom door. In this episode the sink is relocated and the bath/shower is now opposite the bathroom door, for the rest of the series.
The One with the Ick Factor - S1-E22
Continuity mistake: When Monica takes off her belt and throws it onto the couch, it lands on Rachel's arm. Throughout the scene, between shots of Rachel and Monica talking, the belt constantly disappears, reappears and changes position without Rachel ever touching it. (00:05:25)
The One with the Thumb - S1-E3
Continuity mistake: When we first see Chandler in his office, his sleeve is rolled below his elbow. In the next shot, it is above his elbow. (00:12:30)
The One with the Blackout - S1-E7
Continuity mistake: Rachel takes the cat to apartment number 8 and Mr. Heckles opens the door. However, in this episode, the girls' apartment is labeled number 5 which means that number 8 is above them. In later episodes, Mr. Heckles always says that the noisy girls upstairs are keeping him from doing things. [It makes a bit more sense later on in the series when Monica and Rachel's appartment changes to number 20, which is when Mr Heckles starts to complain about the noise (although in the flash back episode when Phoebe is still living with Monica it seems apparent that they actually know Mr Heckles, which Phoebe shows no sign of when she and Rachel are looking for the owner of the cat).] (00:13:40)
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 with All the Poker - S1-E18
Continuity mistake: After the game at Ross' apartment Chandler takes Phoebe's cursed money, and when Ross wants to settle up with "the big Green poker machine who owes fifteen," Rachel's sitting down at the table in front of Ross, but then it cuts to Rachel who's suddenly standing up near the table. (00:12:30)
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.