Audio problem: Just before Frasier opens the door to get his paper, he says "I'll get him for this and his little dog too". However, his mouth moves when he says "I'll get him for this and his...", but his mouth doesn't move when he says "...little dog too". (00:02:40)
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: 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.
Plot hole: Niles makes up Frasier's couch to sleep in and when he lies down he lets out a yelp - and pulls a plastic pirate's hook from behind the cushions. Earlier Niles had appeared wearing a pirate's costume but at no point did he have a hook, nor did he go near the couch. His overcoat had been on the floor the whole time so it couldn't have come from there. It would have been difficult for it to get behind the cushions unless deliberately shoved there, which we never saw and makes no sense anyway.
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.
Revealing mistake: The view from Frasier's apartment shows the Space Needle prominently in the background, however, the elevator that takes visitors from the ground to the observation deck is frozen in time midway to the top. This was corrected after the first season.