Other mistake: In the scene where Rachel is going to take out the trash, Monica tells her the garbage room is the 3rd door on the left. However, when Rachel comes back with the pizza box and Monica leaves for the garbage room, she leaves the apartment and walks towards the right - there are no doors that way, just the stairs.
Revealing mistake: During the end bit, before we get to see Phoebe when she is being interviewed at Lara and Jeni's Massage, if you look closely at the name of the massage parlor, you'll see that, although the camera shakes and bumps, the words stay on the very same spot on the screen. Obviously the canopy was blank and the name was digitally added later.
Visible crew/equipment: When Phoebe and Rick are sat on the massage table, keep an eye behind Phoebe's head when the camera is on her, particularly after Rick says, "I can always find another masseuse." You can see the shadow of the boom mic moving.