Factual error: Monica takes an ovulation test to see if she is still ovulating. The ovulation test only works before you ovulate (usually 24 to 36 hrs), to detect the LH surge that comes before you ovulate. Once you ovulate that surge is gone and the test will not work.
Continuity mistake: When Ross walks in on Sandy and Joey playing the recorders, Joey puts his recorder down on the table in front of him, when Ross storms out of the room, the recorder is in a totally different position and also on the far end of the table.
Revealing mistake: The giant poking device is supposedly long enough to reach right across to the next building, but after they wake up Ugly Naked Guy, Joey says "retract the device!" and after pulling back about a foot of it the end suddenly pops up at the bottom of the screen.
Continuity mistake: When Rachel and Phoebe are talking in the Baby Beauty Contest and Rachel is holding Emma, Emma's head instantly changes position between shots several times, often going through 180 degrees. Clearly they couldn't get her to do the scene in one take and therefore the editing suffers.
Factual error: The restaurant refuses to take anyone's orders until they're all seated, which means that the group is sitting, occupying a table, without earning any revenue for the restaurant. There isn't a restaurant in NYC that would have such a policy, since it basically guarantees that a table becomes a revenue vacuum. (It also makes for very unhappy customers, but that doesn't qualify it as a factual error, since some restaurants might be actually stupid enough to not care about their return customers).
Plot hole: The times in this episode vary a lot. Monica and Phoebe first bet about Rachel giving birth, then it goes to the scene with Joey and Chandler at the movies. It then returns to Monica and Phoebe the next day with Monica losing the bet. However, a little while later, it goes back a day and shows Joey and Chandler at the movie premiere again.
Continuity mistake: Ross, Joey and Chandler are in Chandler and Joey's appartment talking about Ross' decision. Chandler has a green bottle in his hand. He puts it down behind the computer by the microwave, but when Ross starts listing Rachel's "cons" the bottle's suddenly at the opposite end of the counter.
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.