Continuity mistake: At the beginning of the show, Frasier and Niles are in Cafe Nervosa and Roz comes in, with lots of Christmas gifts. She manages to unload them, take off her coat and get into a chair between the guys - all in a couple of seconds. It all happens too quickly for "real time".
Continuity mistake: Frasier's in the toy store and another customer comes in with a carrier bag of educational toys he bought elsewhere. As Frasier tries to talk him into selling him the toys, some shots show just the bag with the toys in it and other shots show a roll of green wrapping paper visible about 6 inches above the bag.