Continuity mistake: There was an episode in which Martin attempts to end a feud between Frasier and Niles by telling a story about his detective partner. He starts with the line, "I never had a brother...", but in the episode about Frasier's cousin Nikos getting married, Martin's brother Walt was introduced.
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: Frasier (and later the others) come back to his apartment to avoid the rain - they shake off umbrellas, and we even hear the storm at the very start of the scene. However there's no rain on the balcony - can't be covered, as we see in "Call Me Irresponsible" during the obligatory sex scene that when it's raining the balcony gets soaked.
Continuity mistake: During the first episode of Frasier there is a painting of some vases in Frasier's apartment which is at the end of the hall leading on to Daphne's Room. In this episode the painting has a red and purple background, however in 'Here's Looking at You' (S1, 2 mins 52 secs) the exact same painting is now red and blue. It remains this new colour for the entire 11 seasons. (00:06:50)
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.