Continuity mistake: Niles and Frasier are at Marty's old apartment and Niles sits down on the couch. Eddie is sitting next to him, staring. During this scene, the shots of Eddie show him moving from fairly close to Niles, to about 10 inches away, and then back again. He has no time to change position naturally.
Continuity mistake: Frasier, Martin, Niles, Daphne, and Diane are having dinner at Frasier's and he gets up to get dessert. Niles offers to help him and puts his table napkin in his chair. As he walks towards the kitchen, though, the napkin is lying next to his plate.
Continuity mistake: At the beginning of the show, Frasier is on the plane sitting next to a woman who finds out he's only on there because he wants to pursue her. She asks the flight attendant if she could change seats - but the shot before showed that the attendant had completely walked by their seat but when the woman asks her if she can move she has not passed their seat yet.
Continuity mistake: Niles has his dog over at Frasier's. He sits down on the couch and the dog is facing the door. The next shows the dog standing about two feet away and facing the balcony - and the third shot shows her back in the first position. There was no time for her to change positions naturally.
Continuity mistake: During the scene where Niles tells the chef to serve the souffle in a large bowl, there is a large bowl of food next to him with no utensil in it. When Niles says "Table Twelve is still waiting for their entree", there is suddenly a utensil sticking up in the center of the bowl.