Revealing mistake: In the episode where Joey is doubling Al Pacino's butt you can clearly see his shadow when he's shooting the scene in the shower, and he's wearing boxer shorts. (00:13:20)
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 with George Stephanopoulos - S1-E4
Visible crew/equipment: When the guy delivers the wrong pizza, in the shot after Monica grabs the pizza box to hand to Phoebe and shouts that they have George's pizza, the tape marks can be seen on the floor with one of them between the delivery guy's feet.
The One with the Dozen Lasagnas - S1-E12
Visible crew/equipment: When Rachel's dumping all of Paolo's clothes over the side of the balcony, we can see the apartment's back wall is only half a wall, with the sound stage and equipment at the left side of the screen.
The One with the Monkey - S1-E10
Visible crew/equipment: While Phoebe's talking about David she mentions the movie 'An Officer and a Gentleman, ' and when she tells them that David is kind of like the guy she went with to see that movie, in the following wideshot the boom mic can be seen moving around at the top of the screen. (00:06:10)
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.
The One Where Rachel Finds Out - S1-E24
Visible crew/equipment: After Monica asks Rachel if there's someone else and shouts, "Why the hell are you dumping my brother?," when it cuts to Chandler sitting at the counter, the edge of the set can be seen at the left side of the screen, and also note the front door is wide open for the camera access. Additionally, when Joey joins Chandler at the counter the juice box has black tape covering its brand name.
The One with the Sonogram at the End - S1-E2
Visible crew/equipment: When Ross announces that Carol's pregnant, after Chandler says, "Kind of puts that whole pillow thing in perspective..." in the next shot of Ross and Monica we can see a crew member's sleeve at the left side of the screen. (00:07:30)
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: 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 Blackout - S1-E7
Revealing mistake: When Rachel first meets Paolo she's looking for the cat in candlelight, holding the candle in front of her. You can see her shadow on the wall, as well as the shadow of the candle, revealing that the light is not coming from the candle. (00:07:25 - 00:14:30)
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 East German Laundry Detergent - S1-E5
Visible crew/equipment: When the horrible woman enters, the boom mike is visible in the mirror at the top of the screen. (00:10:10)
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.
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.