The One Where Joey Dates Rachel - S8-E12
Continuity mistake: When Phoebe is playing Ms. Pacman to erase Chandler's high scores, the door of the apartment can be seen open. When she loses and starts swearing, Ross enters the apartment with Ben, opening the door. (00:19:10)
Continuity mistake: The bathroom in Chandler and Joey's apartment constantly changes in the direction it opens in. Sometimes the doorknob is on the left, sometimes it is on the right. The changes occur throughout the seasons, and in some cases the changes occur in back-to-back episodes.
The One With Monica's Thunder - S7-E1
Visible crew/equipment: When Monica says she's opened the door to the past, a little bit of a stage light is visible above her head.
The One With All The Rugby - S4-E15
Other mistake: When Ross first goes out to play rugby and goes into the scrum, just after Emily talks to the rest of the players, he jumps into the middle of the scrum where the ball should be. Instead, in the next shot, the rugby ball is to the far left of the shot, not in the actual scrum.
The One With Joey's Fridge - S6-E19
Visible crew/equipment: In the scene where Rachel introduces Sebatian to Chandler, Monica and Phoebe, there is a visible boom mic at the top of the screen in the wide shot, right after Chandler says, "Turns out he is kinda funny".
The One With Phoebe's Wedding - S10-E12
Continuity mistake: After Ross greets Phoebe at the rehearsal dinner, he moves toward Mike as if he is going to speak to him. The camera cuts to Phoebe and Ross is now standing behind her, facing away from where Mike is.
The One Where The Stripper Cries - S10-E11
Revealing mistake: During the 80s flashback, Monica and Rachel's cups are obviously empty.
The One With The Embryos - S4-E12
Visible crew/equipment: Near the beginning of the show when Joey asks them who's going to ask the questions a boom mic is visible over Monica's head. (00:05:05)
The One With The Apothecary Table - S6-E11
Continuity mistake: When Phoebe and Ross are talking about Ross buying his sheets at the flea market, Phoebe says, "Ross, come on, you gotta loosen the purse strings a little" with her hands by her side. The camera cuts and her hands are now out in front of her.
The One With Ross's Library Book - S7-E7
Factual error: When Ross shows Chandler the book, he claims it is in "the biggest library on campus" at NYU, which would be Bobst library on Washington Square Park South. Later, in Central Perk, when Ross tells Rachel and Joey about the people "making babies" in front of his book, Joey says, "Wait a minute. Fifth floor, against that back wall?" Bobst's fifth floor is conference rooms only; there are no stacks on that floor. Joey might have been confused, but Ross should know better, being a professor and having just visited that location. (00:08:30)
The One With The Secret Closet - S8-E14
Visible crew/equipment: When Chandler walk in Joey's apartment and say "Rachel's all moved out, huh?" as he walks towards Joey a lot of set lights are visible above their heads. (00:18:55)
The One With The Princess Leia Fantasy - S3-E1
Audio problem: When Monica answers the door and sees her father, she says "Hey Dad, what are you doing here?" but her lips barely move at all.
The One With The Princess Leia Fantasy - S3-E1
Continuity mistake: When Ross gets takes out a Popsicle and says who dated a stripper, he takes a bite of his Popsicle and and the camera cuts to Rachel, then back to Ross and the bite has vanished.
Continuity mistake: The white dog that Joey gives Chandler sometimes has red lips and sometimes does not.
The One With the Male Nanny - S9-E6
Continuity mistake: When Ross says, "Not knowing when to shut up, that's my thing," the amount of pizza he has eaten changes between shots. (00:21:50)
The One With Phoebe's Birthday Dinner - S9-E5
Continuity mistake: Near the start, when Chandler asks if anyone else smokes, a woman with a brown jacket is seen getting a pack of cigarettes out her pocket. The camera cuts and now she has one in her mouth and is lighting it. (00:02:35)
The One With The Soap Opera Party - S9-E20
Other mistake: In the opening credits, the word "Teleplay" is misspelled as "Telelplay."
The One With The Lesbian Wedding - S2-E11
Revealing mistake: The first time we see Rachel's mom in the coffee house, Rachel puts her coat on the hook by the door. When she does this the wall visibly shakes.
The One With The Ring - S6-E23
Plot hole: In the opening scene Phoebe and Chandler discuss how Phoebe knows Chandler is going to propose: by walking in on him whilst he was looking at a ring catalogue on the toilet. However, in the previous episode Chandler leaves the apartment right after he found out about Monica booking the wedding slot (on the answerphone) and doesn't come back until he 'freaks out' at Monica and then it is revealed that it was just put on and Phoebe is in on the plan. It doesn't add up, as Chandler would have had to have been looking at the catalogue between hearing the message and deciding to propose, in the same afternoon when he wasn't even in the apartment.
Suggested correction: Chandler decided at some point before the events of TOW Paul's the Man to propose to Monica (and that's when Phoebe walked in). He likely got Phoebe the passes to the museum (because he's the one that said Ross wouldn't be interested). If you look at the episode again, yes, he is freaking out-ish, but this is to fake out the audience. Also, he's "not the groom" because he hadn't proposed yet.
The One Where Ross and Rachel...You Know - S2-E15
Plot hole: Rachel says she didn't want to wear her glasses on their first date. Rachel doesn't wear glasses.