Revealing mistake: When Chandler grabs his bag he accidentally lets the box full of wedding china fall off the stool. Watch closely (play in slow-motion). The box falls on the floor and shattered china falls out. The china was ALREADY broken before it falls on the ground.
Continuity mistake: When Phoebe sits on the swing (when learning to ride her bike), her scarf has one end down her front and the other over her left shoulder. In the next shot, the end is over her right shoulder instead of her left. A couple of shots later, it is switched back again.
Revealing mistake: When Rachel holds up the Polaroid she took of her assistant, it appears to have been one of the actual photos taken in the earlier scene; you can see the edge of the set behind him, and the overhead lights in the black space to the right of the photo.
Continuity mistake: Chandler is able to get into Monica's apartment to tell everyone that Underdog got away, but later when Rachel closes the door it is now locked. We can see the door as each person is leaving and nobody does anything which could be construed as locking the door before it closes. It's been often demonstrated in the show that the door doesn't lock automatically.
Revealing mistake: When Joey comes in with the shoebox containing the chick, it looks like a normal sized box, about 5 - 6 inches deep. But when Joey takes the lid off, we can see that the chick must be elevated on something inside the box, since we can see its entire body. Surely, the chick can't be more than 6 inches tall?
Continuity mistake: Joey goes into the bathroom and the toilet is behind the door. In a previous episode, when Joey doesn't know about Chandler and Monica, he comes out of his room and thinks it is morning. He goes into the bathroom and Chandler pushes the door open to reveal Joey asleep on the toilet with his toothbrush in his mouth, only the toilet is now on the other side of the room, not behind the door.
Continuity mistake: When Joey and Rachel are trying to work out if the other knows about Monica and Chandler, they sit at the table in silence. In a side shot of Joey they look at each other sneakily, and Joey has his arms by his sides. It then cuts to a head-on shot of Joey, and he's got his right arm over the back of the chair.
Revealing mistake: When Phoebe is looking at the front page of the "Chelsea Reporter," Monica says her restaurant review is on the back page. However, Phoebe doesn't turn to the back page, but merely flips the paper over, looking at the bottom of the front page (and finding the review there).
Continuity mistake: There is a scene in Central Perk where Rachel confronts Chandler about all the kissing he's been doing. She raises her hands up in front of her and tells Chandler to hold on to stop him from getting up from the couch. As he goes to sit back down on the couch she lowers her hands to her lap. The shot cuts to an angle behind Rachel's chair and she is lowering her hands again.