The One With The Red Sweater - S8-E2
Plot hole: They say that whoever the sweater belongs to left it behind, but in The One Where Rachel Finds Out that Ross videotaped them together it is clear that Ross is not wearing anything under the sweater, therefore for Ross to have left it behind he must have gone home topless.
The One With The Stain - S8-E7
Plot hole: When Monica falls off the chair you can see that she is wearing a white bra because you can see some of the cup and the strap (when she says "you're not getting it". Towards the end of the episode (still the same day) we find out that Monica is meant to have the same bra on as their new cleaner, Brenda. The bra she is meant to have on is 'pink with the lacy cup'. Rachel notices that Monica is wearing that bra and she shows Monica. What happened to the white bra she had on a few scenes before? (00:11:15 - 00:19:10)
The One With The Cake - S10-E4
Plot hole: Judy says that both her parents died very young. However, we saw her mother's death in "The One Where Nana Dies Twice" and she was quite old. Also, in Season 7, 'TOW Phoebe's cookies', Jack Geller tells Chandler that his father in law still thinks he is a lawyer and says "So if you ever see me giving them legal advice, just nod along," implying that Judy's parents were both still alive.
The One Where Rachel is Late - S8-E22
Plot hole: The times in this episode vary a lot. Monica and Phoebe first bet about Rachel giving birth, then it goes to the scene with Joey and Chandler at the movies. It then returns to Monica and Phoebe the next day with Monica losing the bet. However, a little while later, it goes back a day and shows Joey and Chandler at the movie premiere again. (00:09:00)
The One With The Birth Mother - S10-E9
Plot hole: David Schwimmer is 6'2" tall and Jennifer Aniston is 5'6". There is no way that clothes that fit Rachel would also fit Ross. When he puts on the clothes that Rachel bought it's obviously not Rachel's size. If it really were, it would be a lot tighter and shorter (Ross could probably wear it belly free).
Plot hole: In TOW Ross tells Rachel he cannot see her following a promise to Emily, the rest of the friends go into Monica's bedroom. Joey hauls out a box from under the bed, saying that he's been hiding it there since Ross said the wrong name at the wedding. Surely Monica, with her obsession for keeping the place clean, would have noticed a box under her bed? (00:04:10)
The One In Barbados, part 1 - S9-E23
Plot hole: This is actually for both parts of "The One in Barbados": it's shown that Monica's hair gets all frizzy from the humidity. And yet she's shown all throughout with her hair out and loose in all its frizzy glory, though it bugs her. I could maybe buy that not one of the women have hair gel with her (not bloody likely.) or that the fancy hotel doesn't sell hair gel (possible). But resourceful Monica would have thought of something to calm down her hair, or she would have just tied it up in a ponytail or bun - she does care a lot about her appearance. It makes no sense other than for comic value. (00:09:30)
The One With Five Steaks and an Eggplant - S2-E5
Plot hole: Chandler has always loaned Joey money for various things (rent, acting classes, Christmas gifts, etc), so he shouldn't be surprised to learn that Joey doesn't have money for fancy dinners or birthday celebrations. Plus, Joey never seems to have a problem taking money/handouts from Chandler - why now? Also, Chandler explains that they're buying Ross a cake ($20), but why doesn't Monica (the chef and his sister) just make him one? (00:07:50)
The One With Ross's Wedding, part 1 - S4-E23
Plot hole: The wedding is threatened because Ross, Emily, and Monica discover that the location has been torn down a few days early. However, when one plans an event, especially a wedding, one puts down a deposit to hold the location, signs a contract, and has all of that in writing. The church would not have allowed the tear-down to happen early as they'd be in breach of contract for accepting money and then allowing the church to be torn down before the wedding. And if they had broken the contract, Monica would have been screaming about it and demanding a refund.
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 Ross Got High - S6-E9
Plot hole: Monica is trusting Rachel to make a traditional English trifle and being a top chef (or an even averagely intelligent human being) she would know what ingredients are used in one. So there's no way she could have missed Rachel cooking beef with peas and onions during the cooking process. Rachel's cooking it right there in Monica's kitchen while everyone else is there!
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 The Ride-Along - S5-E20
Plot hole: When Rachel picks up the box of photos they all fall out, because the box isn't sealed with tape or even folded properly. But there's no way for that to have happened. Monica would have brought the box from somewhere and put it on the couch, and the photos would have fallen out then, and she would have fixed it (this is Monica, after all.) The only way for this to have happened is if she put the empty box on the couch, unfolded/unsealed, and then put photos in it - which Monica would not do.
The One Where They're Up All Night - S7-E12
Plot hole: It is made clear through dialogue in the episode that Joey and Ross are stuck on the roof because Joey removed the bit of piping holding the door open. However, when Tag, Rachel and Phoebe get up to leave, Phoebe says "Shh, get me out of here" and there is a clear shot of the door standing wide open. Afterward, it is possible to see Tag reaching for the door handle to close it behind him. This is inconsistent with the idea that the door needs to be held open. (00:02:20)
The One With Mac & C.H.E.E.S.E. - S6-E20
Plot hole: When Chandler is in Joey's apartment, he answers the phone and says, "Joey's not here right now, can I take a message?" A split-second later, we hear Chandler say, "Yeah, so the audition's been moved from 5:00 to 2:30?" It would be 100% impossible, within the fraction of a second that Chandler is silent, for the other party to pass along the fact that Joey's audition has been moved and the new start time. In fact, there wouldn't have been time to speak more than a couple of syllables. (00:08:45)
The One In Vegas, Part 1 - S5-E23
Plot hole: Ross supposedly can see Rachel while she's walking around naked in her kitchen. Nope: the kitchen is several feet away from the window, and the balcony is also in the way. Ross wouldn't be able to see a thing.
The One Where They All Turn Thirty - S7-E14
Plot hole: There's no way Phoebe has lived to 31 without knowing her birth date. She's had "real" jobs (like the massage parlor) and those require social security numbers and accurate birth dates. She didn't go to high school, but she mentions classmates, so she must have gone to elementary/middle school, and those required birth dates even in the '70s and '80s. She's also "lived in Prague," which she couldn't have visited without a passport - which requires a birth certificate.
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.