Continuity mistake: When Monica's mum and dad are leaving the party, they are standing next to each other while her dad explains why he can not drive anymore. Her mum has both hands in front of her holding on to her purse, in the next shot one arm is around Monica.
Continuity mistake: When Jack and Judy leave Joey's apartment, there is a birthday banner on the counter that has fallen off. When Monica, Chandler, Joey and Phoebe are racing the toys to see who gets to go, the banner is back on. In this time no-one has fixed the banner as there is not enough time for them to do so off camera and the people on camera don't fix it. It's most clear that it's back on when Monica is saying, "Technically, our dog never crossed the finish line".