Continuity mistake: In previous episodes we've seen that from the living room there's a short wall just inside Monica's bedroom (presumably to prevent a clear view inside, as her bedroom set isn't normally there). However in this episode when most of the gang are in her room, they're listening right by the door into the living room with nothing in the way.
Continuity mistake: Just after Rachel goes in to her surprise party in Chandler's apartment, she is talking with Ross and Chandler and says, "Both of them are here?" As she says this, she is facing forwards, yet in the next shot, she is suddenly facing Chandler.
Revealing mistake: In the opening credits for both parts, fat Monica jumps on the couch and it lifts up on Chandler's end. If you look carefully at Chandler, you can see him holding one end of the couch with his hand and pressing up with his foot.
Continuity mistake: Chandler is chasing Kathy down the street trying to get her attention. During a close-up of him running, just before the camera cuts away we see a guy's face on the left; when it cuts back to Chandler he runs for a while and then encounters the same guy (the dog-walker). Also, when he finally lands in front of Kathy, there is a bike rider coming towards them, but as the camera cuts back and forth between the two, the rider never passes them.
Continuity mistake: When Phoebe goes to visit her mum for the first time, before she takes the photo off the fridge the cookie jar has its lid on. After she has taken the photo off the fridge, the lid has come off the cookie jar though there is no way Phoebe senior could have taken it off.
Continuity mistake: During the scene where Phoebe is telling Rachel that Paolo made a pass at her, Rachel unrolls a long length of kitchen roll. During the scene there is a shot over her shoulder where we see that the kitchen roll is as normal and in the next shot we see it unrolled again.
Continuity mistake: In the last scene, Chandler is sitting on the couch in the new apartment, and the rooster is sitting on the back of the couch, with his tail facing the window. When Joey comes running out, the shot of the rooster shows his face toward the window, and then in the next shot he has returned to his tail facing the window.