Continuity mistake: Abbie puts Niles' burning menu in the ice bucket where it remains for the rest of the scene, next to the bottle of champagne. Sometimes the menu is right up against the bottle and sometimes it is an inch or two apart - with no one touching either item.
Continuity mistake: During the opening credits, Frasier is playing the piano and Martin is going through papers on the table. When Marty says "I don't know, Eddie, must you?" there is something pink lying on the table. The shot goes back to Eddie and then back to the table, but the pink item has disappeared.
Continuity mistake: Towards the end of the show, Frasier is explaining to Niles how he was stood up that evening; at the same time he is getting himself a glass of sherry. Niles says, "there was no emergency", we see Frasier repeat the actions to get a glass of sherry all over again.
Continuity mistake: In the opening scene, Roz and Frasier are in Cafe Nervosa, and she is snoozing, while a half-eaten muffin sits in front her. As she wakes up and talks to Frasier, the muffin appears whole again. She leaves and Martin comes in and takes her seat. A shot then shows the muffin as half-eaten again, even though no one has touched it.