Continuity mistake: Niles is at Frasier's apartment, visiting with Marty. He takes some crackers out of his black fanny pack and puts the fanny pack behind him. We see it there when he stands up but there is a shot where there is nothing on the couch behind him. It then goes back to showing the fanny pack.
Continuity mistake: This is a mistake within a mistake: Niles and Frazier are trying to get the wrapped presents out of F.'s apartment and replace them with others, to play a trick on their dad. They are getting completely mixed up, and presents are being taken out and then returned by mistake, mostly by Frasier. At one point Niles has a pile of gifts which he puts down on the table behind the couch - the shot shows him holding them, but the next shot shows a completely different pile of presents, even though it is supposed to be the same pile. Frasier picks this pile up. It soon changes again in the next shots.