The One With Rachel's Crush - S4-E13
Other mistake: Monica supposedly single-handedly changed over the guys' apartment from carpet to polished hardwood in two days. There's no way that someone of her size could have moved all that furniture solo (Rachel didn't help since she's totally surprised), stripped off all the carpet, sanded the wood, stained the wood, let it dry, and then replaced all the furniture, in two days.
The One With The Dirty Girl - S4-E6
Other mistake: When Rachel tells Joey he can't get Kathy another "coupon for an hour of Joey love", you can see Chandler (Matthew Perry) mouthing the words "Joey love". (00:17:21)
The One With The Fake Party - S4-E16
Factual error: Phoebe says in the show that she's three months pregnant. Not only is she way too big for that, but the fetus also kicks for the first time. Women don't feel fetal movement until 16 weeks at the earliest, and for a first pregnancy it may not be until 25 weeks or so.
Suggested correction: Phoebe's size could partially be explained in that she was carrying triplets, though Lisa Kudrow was pregnant in real life, and was further along than her character. Her pregnancy had to be written into the show and the gestation timelines did not match up. Phoebe feeling "movement" could just be her imagination, as her character is supposedly somewhat psychic and often perceives things that are not necessarily discernible to others or isn't even real.
Continuity mistake: When Chandler's partner says she's going to be late for Andrew she has her hands in front of her. Camera changes and now one hand is up by her hair. (00:18:15)
The One With The Giant Poking Device - S3-E8
Factual error: The "very long poking device" that the friends fashion out of chopsticks would never actually work. It has vulnerable points every half-foot or so (the length of the chopsticks) and after a certain point would just break or sag under its own weight at one of the vulnerable points.
The One With Ross's Teeth - S6-E8
Character mistake: While on his date with Hillary, Ross says that he has a five year old son. Ben was born in 1995 and this episode is set in 1999, so Ben should be four, not five.
The One With Joey's New Girlfriend - S4-E5
Continuity mistake: When Ross goes to Amanda's house for a date you see her two children sitting on the couch. The little boy with blonde hair is sitting down, when it cuts to Ross and Amanda talking the boy is standing up on the couch, the next shot he's sat down as Amanda walks out the door.
The One With The Screamer - S3-E22
Factual error: Rachel's date yells at the theater patrons who are in the gang's seats; one of them has D13, and he screams "you're surrounded by even numbers, does that give you some clue?" However, the establishing shot shows they're at the Lucille Lortel Theater, which has odd-numbered seats on the left - the side they're sitting on. It is also a relatively small house and doesn't have a D13; the outermost seat in that row is D9. (00:04:50 - 00:05:30)