Continuity mistake: When Phoebe is talking to Ursula's fiance Eric, he is wiping sweat off his face with a napkin. He puts the napkin to his eye and then in the next shot it changes to the other eye without him having enough time to change it. This happens again when at one point he's wiping his eye and then suddenly his forehead.
Continuity mistake: When Rachel returns from running after the boy that she told to "shut up", you see Joey picking up a piece of food, sniffing it and making a face and then putting it back on the tray. However in the next shot, without moving, Joey is munching on something - he didn't have anything in his hand before.
Factual error: This show is set in October (it's a Halloween party). Rachel's stomach is completely flat, but according to the show, she got pregnant in April (It's stated several times by the characters on the show that Monica and Chandler's wedding was in May, and we learn in "The One With the Red Sweater" that she got pregnant a month before the wedding. Hence, April). However, by October she should have a six months' pregnant belly, which is no way resembles the perfectly flat belly she shows.