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.
Continuity mistake: Near the end of the show, when Roz is telling Frasier about Lupe Velez, the wall clock in her booth shows the time to be 3:45. About 5 minutes pass, although the story only takes a couple of minutes, and there is no other action in the scene. The clock actually goes backward after that, showing 3:50 and then about 3:48 in the next shot.