Other mistake: In the scene where Rachel is talking to Chandler in the hall, after she says "the 4th of July", it cuts to a shot from behind Rachel's head. If you look on the right hand side of the screen, you can see a piece of wood in the foreground. This probably came from Joey and Chandler's doorframe, through which this view would have been filmed. In addition, this door was supposed to have been closed throughout the entire duration of this scene.
Plot hole: When Monica falls off the chair you can see that she is wearing a white bra because you can see some of the cup and the strap (when she says "you're not getting it". Towards the end of the episode (still the same day) we find out that Monica is meant to have the same bra on as their new cleaner, Brenda. The bra she is meant to have on is 'pink with the lacy cup'. Rachel notices that Monica is wearing that bra and she shows Monica. What happened to the white bra she had on a few scenes before?
Continuity mistake: After Chandler has been playing the Ms Pacman machine all day he claims his hand has seized up and it appears to look like a claw. From then on in that scene, his hand manages to move around fine. It goes in his pocket, and he waves it around like normal, and then when he mentions his hand again at the end of the scene, it appears to have seized and is clawlike again.
Factual error: The main part of the episode is played out in Chandler & Monica's hotel room (which is situated in between Rachel's and Ross's rooms). The window is opposite the audience and the door on the right. However whenever we see inside Ross's hotel room, he has a window opposite the audience as well. This is impossible as this should be where the hallway is to get to the main door to Chandler & Monica's room. Also, throughout the episode Monica, Chandler & Phoebe all listen through the walls (on either side of their room) to what the other friends are saying, meaning there must be no gap between Ross's and Chandler & Monica's rooms- making the window in his room geographically impossible.
Continuity mistake: In the scene with Robin Williams and Billy Crystal, there is a shot of Rachel, and her hair is hanging straight down. The next shot of Rachel is from a different angle and there is a section of hair behind her ear; in the shot after that it is hanging straight again, and is then behind her ears again.
Factual error: When Monica rolls an 8 to buy everyone a steak dinner, the one die is positioned with a 5 and 4 facing the camera (the 5 on the left, and 4 on the right). With the die that way round a 1 is always on top. There is no other way to get the 5 and 4 combo. This means that Monica had a 7 on the other die, That is impossible. And so she did not roll an 8.