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: Frasier is just saying goodbye to Niles and we can see the brochure for Daphne's reception to the left of his sherry glass. When he stands up and shouts "Daphne!" the brochure has moved about 6 inches to the right, even though no one touched it.
Continuity mistake: While Martin is saying grace, Eddie is sitting right on his backside staring at Frasier, who yells "will you stop staring!" The next shot, from behind Eddie, shows him noticeably leaning over on one haunch, even though there was no time for the change.