The One Where Ross Dates a Student - S6-E18
Other mistake: Ross' semester supposedly just ended, and he's handing in his grades. But the episode just before this one was about Valentine's Day, and the one immediately after this one is about spring break, so this episode is happening sometime between mid - February and March/April. It doesn't matter when the show was aired or produced; Valentine's day is still in February. There's no semester that ends at that time of the year, and NYU wasn't on the quarter system then.
Suggested correction: This episode (production code 225567) was produced before episode 17, "The One With Unagi", (production code 225568) and just aired out of order. So this episode happens before Valentine's Day.
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 Blackout - S1-E7
Other mistake: When Ross and Rachel are out on the balcony alone for the first time, there are no lights on in NYC apart from candle lights. Look in the BBQ behind them though to see a very bright and very white light reflected in the paintwork. (00:13:50)
The One With All The Kissing - S5-E2
Continuity mistake: A few days after the friends have returned to New York following Ross' wedding, Monica's hair is suddenly about three inches longer and a completely different style than it was in London. It was previously just above her shoulders in a sleek "pageboy" style. Once back home, it is much bushier and longer, well over her shoulders. This was obviously due to Courtney Cox growing her hair during the break in-between Season 4, which ended with the Ross/Emily wedding debacle, and Season 5. (The first episode of Season 5 was filmed the previous season and was Part 2 of Ross and Emily's wedding).
Character mistake: Even though both Ross and Rachel have cell phones with them and use them for other calls, it never occurs to Ross early on and as he's frantically racing to the airport with Phoebe, to call and tell Rachel that he loves her or at least to say that he is on his way to tell her something important before her plane takes off for Paris.
The One Where Ross Got High - S6-E9
Continuity mistake: When Rachel tells Phoebe that she's making a traditional English trifle, Monica's holding a cloth napkin, but in the next shot the napkin's suddenly gone and she's now holding forks.
Other mistake: In "TOW the cheap wedding dress" the whole episode is about how Chandler wants "The Swing Kings" to play at the wedding, because, at their concert, that is where he realised that Monica was the woman he wanted to dance all his dances with, and Monica goes to great lengths to secure the band. In this episode, the band at the wedding is actually called "Jungle Swing".
Suggested correction: So the band changed their name in the interim. It happens.
The One Without The Ski Trip - S3-E17
Continuity mistake: At the start, just as Rachel is leaving Joey's apartment after mentioning the tickets she's got, Joey stops her and she turns round. Her hands are clasped together in front of her chest in one shot and by her side in the next. (00:04:00)
The One The Morning After - S3-E16
Continuity mistake: When Rachel asks, "When did Chloe leave?" the paper Ross is holding changes direction. Note the title of the paper: The New Yorker. (00:13:30)
The One With The Football - S3-E9
Continuity mistake: When they are outside for the first time, you see a shot from behind Monica, Joey, and Chandler. Monica then says, "Bring it in," and the shot changes. However, all 3 are now in different poses to what they were in before. (00:04:40)
The One With Phoebe's Ex-Partner - S3-E14
Continuity mistake: When Phoebe says you never run on a barge, her hand changes position on the table between consecutive shots. (00:06:50)
The One With All The Thanksgivings - S5-E8
Continuity mistake: The emergency room doctor's rubber gloves come and go between shots.
The One Where Ross And Rachel Take A Break - S3-E15
Visible crew/equipment: When Ross is on the phone to Rachel, near the start, just as he walks into the living area, a stage light is visible above him (only visible in fullscreen version). (00:06:10)
The One Where Monica and Richard Are Just Friends - S3-E13
Continuity mistake: When Monica is dabbing Richard's shirt, the way she is holding the cloth changes between shots. Note the amount over her fingers. (00:08:50)
The One With Ross's Inappropriate Song - S9-E7
Continuity mistake: When Chandler turns around and Joey watches the football game, the door to Chandler and Monica's room is open. However, when Joey sees the sex part of the tape in the next shot, as Chandler is about to turn around and the TV screen is visible, the door is shut. (00:14:29)
The One With Phoebe's Uterus - S4-E11
Revealing mistake: Phoebe already has a visible baby bump before she even agrees to get pregnant.
The One In Massapequa - S8-E18
Continuity mistake: When Monica shows Chandler the photo of Chi-Chi, as she says, "It's good stuff, huh," in the closeup Monica takes hold of the photo with her raised empty right hand, but in the next wide shot Monica is holding a Sharpie in her right hand and the photo is in her raised left hand. (00:02:25)
The One With The Stain - S8-E7
Continuity mistake: After Gunther responds to Ross with the biting "ezels" retort, it cuts to Monica and Brenda in the living room, and when Monica falls off her chair, the rug and blue pad underneath are suddenly rolled up at the corner, then the rug is properly flat. (00:11:15)
The One Where Ross Hugs Rachel - S6-E2
Other mistake: In this episode, Chandler says that "when it comes to sweets, [Joey] is surprisingly strict" and doesn't allow sweets around the house. Except that in Season Five, "The One With The Kips," we see that Joey leaves Rollo candies everywhere.
The One with the Monkey - S1-E10
Visible crew/equipment: When Joey the Elf deliberately jingles his elf shoes, Chandler's head may explode because of all the unspoken mocking jokes. It then cuts to a shot of Marcel, and the trainer's hand is visible in the bottom left corner of the screen. (00:07:25)