The One with the Fake Monica - S1-E21
Factual error: The monkey is allowed outside his cage at an airport gate. Animals, with the exception of assistance dogs, cannot be transported in the cabin with passengers, and this rule applied in the 1990s as well. There is no way a monkey would be brought through a security checkpoint into a terminal concourse of a NYC airport and allowed aboard a regular commercial airliner.
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 Ick Factor - S1-E22
Continuity mistake: In the scene where Chandler and Phoebe come into the coffee house from Phoebe's first day as his secretary, Phoebe makes no discernible effort to order - but after Chandler says it pays to know the man who wears his shoes the shot cuts to her holding a large latte cup which was not visible earlier in the scene. (00:07:00)
The One with the Ick Factor - S1-E22
Continuity mistake: Monica is in her apartment with her boyfriend and they are kissing, and she invites him to stay the night. Watch the glass of wine she has poured herself: the amount of wine in the glass keeps changing. (00:08:45)
The One with the Ick Factor - S1-E22
Visible crew/equipment: When Rachel is telling everybody about the dream she had with her, Chandler and Joey in it, Ross stands up and starts talking. When he does, the stage lights are visible in the TV. (00:13:40)
The One with the Ick Factor - S1-E22
Visible crew/equipment: In the scene when Rachel is sleeping next to Ross, you can see part of the mattress behind the sofa which cushions his fall later on when he trips. (00:20:40 - 00:22:55)
The One with the Ick Factor - S1-E22
Visible crew/equipment: After Ethan and Monica talk about "at gunpoint" being a place, when Monica asks Ethan to stay over it cuts to a shot facing Ethan and we can see that the back wall is less than half a wall.
The One with the Ick Factor - S1-E22
Revealing mistake: In the scene where they are in the coffee shop talking about Rachel's dream about Chandler. Rachel is carrying a coffee pot around then sits down. When she sits she puts her hand under the coffee pot, which would be extremely hot if it were real.
The One with the Birth - S1-E23
Character mistake: Outside the room in the corridor where Carol is waiting to deliver her baby, the poster outside giving directions says "Nusery", not "Nursery". (00:02:15)
The One with the Birth - S1-E23
Continuity mistake: In the scene when Carol is giving birth, there is a shot when Carol shouts "Where were you?" Her trousers are visible under the sheet. (00:16:25)
The One Where Rachel Finds Out - S1-E24
Continuity mistake: When Rachel and Monica are discussing whether or not Rachel should meet Ross at the airport she's taking a bottle of red wine out of the refrigerator, but when she places it on the table in the next camera shot the bottle of wine is suddenly a bottle of white wine. (00:16:25)
The One Where Rachel Finds Out - S1-E24
Visible crew/equipment: When Rachel is on the balcony with her date, after she kisses Ross and says, "Wow!", the shot changes back to her date. While he is saying, "Exactly" you can see a camera man on the left side of the screen. Then when the shot changes to show Rachel and her date you can see him move out of the shot. (00:19:45)
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 Where Rachel Finds Out - S1-E24
Visible crew/equipment: When Rachel leaves the apartment to catch Ross before his flight, just as she opens the door a crewmember's sleeve and equipment are visible at the left side of the screen.
The One Where Rachel Finds Out - S1-E24
Other mistake: When Rachel leaves the apartment to pursue Ross to the airport, she is turning to the left when she exits the apartment. The stairs are to the right.
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
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
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: 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
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.
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.