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.
Visible crew/equipment: When Monica is waving around her shellfish hairdo in the final scene at the hotel, the camera zooms out. When it does this, look at the top of the set. Not only can you see where the set ends, but you can also see the stagelights, hanging equipment etc.
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: 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: In the one where Rachel is in the hospital after having Emma she is in the bed feeding Emma and Ross is sitting right beside of her. They are talking about their relationship and what should come. If you will watch each shot as they go to showing Rachel's face then Ross's you can see that Rachel's hair in one shot is in front of her shoulder and the next shot it is behind her shoulder. This happens several times.
Visible crew/equipment: When Monica, Ross, Chandler and Rachel are at the apartment and Rachel is suggesting how funny Chandler is, as soon as Ross says, "Sweetie, calm down it's going to be OK," a boom mic can be seen for a short period of time, at the top of the screen.
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.
Continuity mistake: When Monica comes in and asks Chandler if she can borrow some milk, Chandler is reading a paper that is flat on the bar. In the next shot he is holding it folded, then he lays it on the counter, and suddenly it is in his hands again.