Continuity mistake: When Rachel finds out that Ross and Julie are getting a cat, watch Rachel's neck. When she says "together?" she's not wearing a necklace; cut to Ross and Julie for a fraction of a second, then when it cuts back to Rachel saying "both of you?" she's suddenly wearing a necklace. It then disappears again when she says "isn't that just lovely?"
Visible crew/equipment: Chandler and Joey are spending time with Richard; as they play foosball and Richard scores, he leans back and says "Could that shot BE any prettier?" in a mockery of Chandler. The end of the wall and the hallway behind it are visible (ie the wall set ends).
Continuity mistake: When Monica is trying to cheer Joey up, she tells him that she straightened out his shower curtain so it wouldn't get mildew. But in a previous episode (The One Where Eddie Moves In), Joey gives the gang a tour of his new apartment; the shower is clearly visible in the bathroom, and it has a door.
Continuity mistake: The prom video has just ended and the TV screen goes blank. Monica had been sitting next to Rachel, but in the reflection of the TV screen you can see her beginning to stand up. We cut back to a 'real' view, and she's sitting down; then she stands up again.
Visible crew/equipment: When Phoebe goes to visit her father, there is a little dog outside. Phoebe gets back in the car and the dog jumps up the side of it. When he finally gets part way through the window, the top of the dog-handler's head is visible through the car window.
Factual error: The symptoms (spots, fever, etc) of chicken pox only develop 2 - 3 weeks after exposure to the virus. Therefore, when Ross knew that Ben had chicken pox, Phoebe shouldn't have developed the condition until at least two weeks later, and Ryan certainly shouldn't have developed the disease until the end of his stay (as Phoebe was his only contact with the virus).
Visible crew/equipment: During the prom video, Monica, Rachel, and Monica's date Roy are standing in the living room. When Roy leaves the room saying, "I'm gonna kick Chip's ass," the camera follows him out, but as it's turning the boom mic operator is visible. He's kneeling on the floor sliding the mic toward the girls.
Continuity mistake: When Chandler is sitting in his kitchen with Monica and Phoebe, talking to the woman on his computer, the camera is on Monica, showing part of the computer screen. The screen is blank, indicating that the computer is off. In the next shot, the sound of an instant message is heard, indicating that the computer is in fact on.