Continuity mistake: Daphne gives Marty a brightly coloured sweater for Christmas and after he opens it, he puts it back in the box - the yellow sleeve is hanging out. After he says "all that makeup on my face", the sweater has changed position and there is a red portion hanging out of the box. No one touched it in the meantime.
Continuity mistake: Daphne puts a couple of Christmas bags on Marty's chair; the one facing the camera has a Santa on it and behind that are pieces of pink paper sticking up about 6 inches. The pink paper is sometimes visible, and sometimes isn't, as the scene progresses, from the same angle.