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: At the beginning when Rachel falls and starts bleeding, you can see that the wound is somewhere up above her forehead because the blood is running from the wound up there. However, throughout the rest of the episode she has a bandaid going horizontally across her forehead, nowhere near where the apparent wound was.
Continuity mistake: Monica and Chandler are in their apartment talking about Monica's worries that Chandler would dump her if she put on weight. When we first see Monica, the bite mark in her apple is quite small, but a few seconds later, it is suddenly much bigger without her eating any more of it.
Continuity mistake: As Chandler meets Monica at the altar, Monica's hand switches from holding Chandler's hand, to holding the flowers, with no time to do so.
Continuity mistake: During the countdown to midnight, just as everyone says, "Happy New Year!", the camera cuts to Phoebe and Ross. In the background Joey and Rachel open their arms to hug each other; the camera cuts to just Joey and Rachel and they open their arms again.