Continuity mistake: Frasier goes to get a newspaper out of the curbside kiosk, and catches his jacket in it. He places the newspaper to his right on top of the rack beside it and the shot changes to Regan coming out of the florist behind him. Then we see the newspaper in his left hand, without having time to have picked it up.
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.
Continuity mistake: Frasier gets caught in Daphne's room for the second time and crouches down beside her bed with the quilt over his head. He then sneaks into the bathroom - the quilt is left hanging over the edge of the bed. Shortly afterwards he runs out of the bathroom and the quilt is now folded over, completely on top of the bed, even though no one went near it. (00:13:30)
Continuity mistake: As Frasier and Niles are starting work on their book, Marty gets four snacks and a beer and sits down in his chair. He gets up and we see the two bags that were behind the beer and can of something are now in front of them. Marty never touched them during that time.
Continuity mistake: When Roz's date Ted returns her purse to her apartment, Bulldog answers the door. He barks at Ted and Ted nervously drops the purse. We see Bulldog close the door. He should have picked up the purse first, or he wouldn't have been able to close it. We do see him drop the purse in a chair as he heads to the kitchen, but we never actually see him pick it up.
Continuity mistake: Early on in the show, Frasier and Martin are having breakfast and we can see an orange napkin in Marty's lap. While he is talking, the camera angle behind his shoulder shows his left hand against his cheek. Right after that the napkin appears on the table to the left - with no time for him to have moved his hand and put it there.