Revealing mistake: When Rachel is doing the shuffling trick, it is clear that it is a trick deck. The cards, whilst flying from one hand to the other, change the angle of flight in mid-air, and some of them even move backwards as she moves her hands further apart from each other. This could only happen if the cards were connected to each other.
Continuity mistake: When Paulo comes out of Rachel's bedroom to greet the group, the robe he is wearing is obviously untied and hanging open. After we see how everyone reacted to him being there, we again see Paulo but now the robe is securely tied even though neither he nor Rachel changed positions between shots.
Continuity mistake: In the bar, Kathy is trying to set Chandler up with one of her friends. When the camera is facing Chandler, we see Kathy's hand rubbing Joey's back, but when it cuts to a front shot of Joey and Kathy, her arm is down in front of her. Then without having had enough time to move, her elbow is up on the table and she is holding hands with Joey.
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.