The One With The Princess Leia Fantasy - S3-E1
Other mistake: When Phoebe makes fun of Ross' Princess Leia fantasy with the rolls, Rachel tries to stop her; the shots used are the same action, just from different angles. Look at Rachel's hands and the towel in her hand when Phoebe puts the rolls by her ears.
The One with Two Parts: Part 2 - S1-E17
Other mistake: Rachel is limping in the hospital for the first time. When she gets back home, she walks perfectly fine. Then in the hospital, she starts to limp again.
Other mistake: When Rachel attempts to board the plane the first time, the man at the desk looks at her passport upside down.
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.
That's an explanation, but it doesn't make it not a mistake.
It does indeed not make it a mistake, as episodes airing out of order is done by the studio and is no fault of the show's writers.
That doesn't change the fact that semesters end in December.
The One with the Blackout - S1-E7
Other mistake: Phoebe says she was last to know Monica had a crush on Joey when he moved in and Joey acts as though he never knew this. However, when we see him moving in a later episode, he knows Monica has a crush on him, and he is under the impression that Monica wants sex and so strips off in the living room while Monica is preparing some drinks for the pair. (00:13:10)
Suggested correction: I may understand the situation but please do correct me if I'm wrong. Basically in the flashback episode they saw each other in the hallway and smiled at each other. They would've both got the impression that the other one liked them. However, after the lemonade incident he would have then got the impression that he was wrong and Monica didn't actually like him. Finally, Joey heard that she did like him and got a bit confused and a bit happy at the same time.
The One With The Free Porn - S4-E17
Other mistake: The new York to London time sequence makes no sense. The friends are all wearing the same clothes throughout most of the episode. Emily flies from London back to New York and Ross flies to London, most trans Atlantic flights are overnight. It's very unrealistic that Ross got to London in the same day, and she flew back so quickly after getting back to London' even though Ross had only just said goodbye to her. The characters' clothes show this is all taking place in the same day.
The One With Ross's Wedding, part 2 - S4-E24
Other mistake: When Emily first walks in wearing her wedding dress, there is a distinctive difference between that dress and the one Monica picked up from the store a few episodes earlier and tried on (yes, more than that she is also wearing a jacket). There is a band of material at the top of the dress when Emily is wearing it that was not there when Monica wore it.
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)