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.
Continuity mistake: When Chandler, Ross and Monica are in Central Perk discussing playing bagpipes, and Ross says, "Decide whatever you want," he is gesturing with his right hand up and with an open book in his left hand. When the camera angle changes, the book is closed and is now in his right hand.
Continuity mistake: When Ross comes back to Monica and Rachel's apartment and Rachel tells him she has lost Marcel, he takes off his overcoat and lays it over the back of the sofa and then sits by it. As the scene continues, the sofa is still visible in some shots and the black coat is crumpled up on the sofa cushion.
Continuity mistake: In the scene where Monica is explaining to Rachel that she has hired her friend Wendy as her waitress, Rachel is holding a water bottle in one hand and the cap in the other. Monica moves towards her and Rachel is pointing her hand in Monica's direction and then in the next shot we see Rachel from another angle and her hand is holding the cap on top of the bottle too fast to have happened in normal time.