Continuity mistake: When Rachel finds out that Ross and Julie are getting a cat, watch Rachel's tray. When she says "together?" she's got a towel that is flat; cut to Ross and Julie for a fraction of a second, then when it cuts back to Rachel saying "both of you?" it's now in a pyramid.
Continuity mistake: In the second scene with Phoebe and Rachel in the night class, when the camera looks over Rachel's shoulder, she has "Jane Eyre" in her hand face up, but when the angle switches to front view, she has nearly placed the book on the desk.
Continuity mistake: When Joey and Angela talk in Central Perk, the black waitress with long hair is visible the background of shots of Angela. When we see shots of Joey the same waitress is also behind him near Gunther. She is in two places at once.
Continuity mistake: In the scene where Chandler and Phoebe come into the coffee house from Phoebe's first day as his secretary, Phoebe makes no discernible effort to order - but after Chandler says it pays to know the man who wears his shoes the shot cuts to her holding a large latte cup which was not visible earlier in the scene.
Continuity mistake: The gang enters Monica's apartment and it is full of dead Christmas trees. After everybody has entered the apartment we see that the apartment door is shut; the shot then changes to the gang around the sofa, but in the next shot when Rachel answers the phone we can see behind her that the door is open.