Continuity mistake: When Ross and Rachel are arguing about Rachel telling Phoebe about his fantasy, Ross takes a popsicle out of the freezer and bites it. In the next shot, the popsicle is whole again, with no bites, and Ross takes another 'first' bite out of it.
Continuity mistake: When Joey says "we'll call that plan B, all right?", Monica has her chin in her hand. When it cuts to a different angle, she's got both arms on the table. Rachel also goes from having both hands clasped under her chin to having one arm resting on the table and one reaching for coffee.
Continuity mistake: Near the start when Janice is touching Joey's cheek in his apartment, Joey is seen from the front, and he is not holding anything in his hands. He is then shown from the side and he is holding a box of cookies or something similar.
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.
Continuity mistake: When Rachel and Phoebe are in Central Perk talking about the Princess Leia Fantasy, a guy in a yellow shirt and white pants is standing at the bar behind Phoebe. As they talk he walks to the door and leaves, but in the next shot he is standing behind Phoebe again, just as she says "That's the moment when she becomes a woman."
Continuity mistake: S3E1; Ross is telling Chandler about how woman tell each other everything in Central perk. Chandler puts a book about trout on the table and then talks to Ross, then the camera zooms out and the book has moved more to his left and a coffee mug is in front of it.