The One With Rachel's Going Away Party - S10-E16
Plot hole: In this episode Chandler finds furry black handcuffs, and everybody says that they have never seen them before. How is that possible considering all the people that have moved in and out of that room? How come nobody noticed them when the room and closet were painted green after being pink?
The One Where Monica Gets a Roommate - S1-E1
Revealing mistake: As Monica is walking to her room and steps on Paul's watch, if you look carefully, you can see that she just steps on the band. That would not damage the watch. (00:26:45)
Factual error: The makeup on Rachel's face "can't be covered up with makeup," and "won't come off," we learn in The One In Vegas, Part 2. So it's not a surprise that she still wakes up with it on (and so does Ross.) but an hour or so later, when she's at breakfast, it's not there. An hour or two won't make the magical difference that 8+ hours didn't.
The One Where Joey Moves Out - S2-E16
Other mistake: When Rachel is showing Phoebe her heart tattoo, the tattoo isn't dressed and covered, nor is the skin around it red or swollen, despite the fact she just finished getting it. (00:14:09)
The One Where Joey Dates Rachel - S8-E12
Factual error: When Chandler is explaining that he played Ms. Pac Man all day, the Ms. Pac Man machine is unplugged, and then plugged back in. Immediately upon being plugged back in, we hear the Ms. Pac Man theme song being played. No version of a Ms. Pac Man stand-up arcade ever played the theme song upon powering on. Instead, it would silently go into "demo mode." The only way the stand-up arcade version of Ms. Pac Man would ever play its theme song was after two events occurred in order: 1. A coin was dropped in the slot (or a button was pressed on the inside of the unlocked coin drawer), and then 2. Someone pressed the '1 player' or '2 players' button to start the game. It is clear that neither of these things has happened in the scene by the time the music starts playing. (00:11:50)
The One With The Home Study - S10-E7
Other mistake: In the opening scene Chandler smiles at Ross' joke while playing with the ball in his hands. Later on in the scene Ross cracks another joke and the exact same scene of Chandler smiling and fiddling with the ball is repeated. (00:00:40 - 00:01:10)
The One With The Stain - S8-E7
Continuity mistake: When Monica asks Brenda to clean the top of the cabinets so that she can get a look at her crotch, Brenda drags a chair over (with both hands) to stand on. In the next shot, she is magically holding a feather duster. (00:11:40)
Other mistake: When Joey announces that he has a job in the new Al Pacino movie, Ross is holding a bottle of peach Snapple with part of its brand name whited out, so it reads "S pple" on the label. (00:13:50)
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 The Giant Poking Device - S3-E8
Revealing mistake: When Monica and Rachel are banging their heads on the wood, it is clear that they aren't hitting them hard enough to result in the winces that are apparent. (00:09:00)
The One With The Princess Leia Fantasy - S3-E1
Plot hole: In the beginning the Friends enter Central Perk and see that there are some other people on their couch. Monica looks fine and happy - even though later in the episode the other Friends say that she's been depressed for some days now, and she doesn't leave her apartment.
The One With All The Resolutions - S5-E11
Character mistake: In one of the scenes where Phoebe is teaching Joey guitar, she asks him to demonstrate the "Iceberg" chord. To refresh his memory, Joey refers to the chord as "G Sharp." In reality, the only way to play a G Sharp chord is with a barre chord, and as such the fingering is not exclusive to it.
The One Where Everybody Finds Out - S5-E14
Continuity mistake: In the scene where Chandler turns on music when he and Phoebe are going to "have all the sex" you see Phoebe's arm begin to move in the right corner of the screen. When it cuts to her she has not yet begun dancing, and when he goes to turn the music on again it is a duplicate clip from the initial shot.
The One With the Pediatrician - S9-E3
Continuity mistake: In the scene where Phoebe asks Mike to prove that he plays piano, his arm goes from resting on the couch to on his lap from one shot to the next. After Phoebe tells him "You are really good," his left arm is resting on the couch. But in the next shot when Phoebe continues talking, his arm is resting on his lap.
The One With Mac & C.H.E.E.S.E. - S6-E20
Continuity mistake: In the episode before, Rachel's hair is just underneath her shoulders. Then, a few weeks later when Ross gets back from Spring Break, it's a lot longer than before.
The One Where Rachel Tells... - S8-E3
Visible crew/equipment: When Monica is yelling at the other couple on their honeymoon, the things on the shelves behind them shows the reflections of set lights. (00:15:25)
The One Where Old Yeller Dies - S2-E20
Continuity mistake: A woman and a man in a blue shirt exit the coffee shop twice.
The One With The Bullies - S2-E21
Continuity mistake: A woman and a man in a blue shirt exit the coffee shop twice.
The One With The Bullies - S2-E21
Visible crew/equipment: While driving the cab, Phoebe is wearing a blue shirt. When the car stops suddenly, a crew member wearing a white shirt is visible driving the car.
The One With The Halloween Party - S8-E6
Audio problem: When Rachel greets Mona at the door of the apartment, visually she says "Hi" but the audio is " Hi Mona. "
Answer: The painting doesn't have a name, and if it does it is never mentioned in this episode.