Continuity mistake: When Rachel and Monica knock on Danny's door and he opens it, there is a wall a few feet behind him. Later, when Rachel shows up at Danny's apartment to cancel their date, she enters into an open room and there is no longer a wall in front of the door. Danny's apartment is supposed to be one floor directly below Chandler and Joey's apartment. This was obviously the same set for their apartment that was used for Danny's and the wall was added for that shot to disguise it.
The One With The Inappropriate Sister - S5-E10
Continuity mistake: When Rachel and Monica are arguing about her meddling, Monica raises her hand to her face and you see a sparkly engagement ring on her finger. Her character wasn't engaged but Courteney Cox was at the time. (00:07:05)
The One With The Ultimate Fighting Champion - S3-E24
Continuity mistake: Joey's hair is suddenly much shorter after the intro with Robin Williams and Billy Crystal - everyone's wearing the same clothes so no time is meant to have passed.
The One With Rachel's Dream - S9-E19
Continuity mistake: When Rachel is telling Monica about her dream at Central Perk, Phoebe enters and leaves her bag on the couch but it falls. However, in the next shot, her bag is right at her side on the couch. (00:14:40)
The One With The Proposal, part 2 - S6-E25
Continuity mistake: Right after Monica says, "You wanted it to be a surprise", the camera pans to Joey who shuts the door firmly, however in the next shot you can see the door gliding back open and then shutting again. (00:18:40)
The One Without The Ski Trip - S3-E17
Continuity mistake: When Phoebe is saying how she gets out of tickets, she is pointing at herself in one shot and not in the very next shot. (00:05:50)
The One With The Football - S3-E9
Continuity mistake: At the end, Chandler points at Joey, and when he does so, his sleeve goes from rolled down to rolled up instantly. (00:22:10)
The One With The Football - S3-E9
Visible crew/equipment: Just before Monica tackles Chandler to the floor, there is a shot with a very large boom mic visible at the top of the screen (only visible in fullscreen version). (00:13:10)
The One With The Football - S3-E9
Continuity mistake: Chandler says he's been preparing for something his whole life. When he says this, his right sleeve is rolled up. Camera changes, and now it's rolled down. (00:10:40)
The One With The Football - S3-E9
Continuity mistake: When Joey tells Chandler to prepare to feel very bad about himself, he has the football in his right hand. When the shot changes, it's in his left. (00:10:30)
The One With The Football - S3-E9
Continuity mistake: When Joey introduces himself to the Dutch lady, the way and where he holds the football changes between successive shots. (00:08:40)
The One With The Football - S3-E9
Continuity mistake: When Rachel asks Ross if not catching Joey was part of his football strategy, she has her hands outstretched in one shot and then on Ross' shoulder in the next. (00:07:10)
The One With The Football - S3-E9
Visible crew/equipment: When Ross is explaining the playing area near the start, the boom mic once again dips into view and follows him (only visible in fullscreen version). (00:05:40)
The One With The Football - S3-E9
Visible crew/equipment: Pay close attention when we see the gang outside for the first time. In the upper left-hand corner, you can see a boom mic moving about in the shot, clear as day. (00:04:30)
The One With Rachel's Big Kiss - S7-E20
Other mistake: Matthew Perry supposedly really likes wearing a tux that turns out to have been made for Diane Keaton. Except that Diane Keaton is 5'7" and Matthew Perry is 6 feet tall, and also considerably larger than the very slim Diane. He wouldn't even be able to put it on.
The One With The Free Porn - S4-E17
Factual error: We know that Phoebe is three months pregnant, because it's the day after the party where she told Joey that she was three months along. But the ultrasound shows three little lumps that in no way resemble a three-month fetus. An actual three-month fetus is the size of a jellybean.
The One With Phoebe's Cookies - S7-E3
Character mistake: When Phoebe brings in her frozen cookie and Monica tastes it to try to determine the ingredients, she says "I definitely taste nutmeg." She then goes on to brag about how that's the difference between a professional and a layman. Except that later when she finds the actual recipe, it's from the Nestle Toll House bag - and that contains no nutmeg.
The One With The Ball - S5-E21
Factual error: There is no way that a cop and a masseuse could have afforded an apartment in Brooklyn Heights, even in the '90s. (Brooklyn Heights was unaffordable in the '80s.) "Rent control" doesn't explain it either, as a vacant apartment - which is what they are looking for - would be raised to "market rate" if a rent-stabilized tenant moved out. This can't be written off as a character mistake: Gary is not naive or uninformed, and his accent makes clear that he is a New Yorker.
The One With Monica and Chandler's Wedding, Part 1 - S7-E23
Continuity mistake: When Monica and Chandler walk toward the middle of the room the camera cuts to Ross talking to his parents saying that he could kick Chandler's ass, Behind them are Monica and Chandler in a different place, listening and laughing to Ross. (00:10:50)
Suggested correction: The shot is continuous. There is no continuity mistake.
The One With the Pediatrician - S9-E3
Continuity mistake: Ross' broken finger disappears overnight. It's broken in one scene, not broken in the next scene which takes place on the same or next day.