Continuity mistake: Niles says on Daphne's wedding day that he told her he loved her on his 3 day anniversary, making Daphne's wedding his 4 day anniversary. At Nervosa, Mel says it's their 4 day anniversary, when at this point one more night has passed and it's now 5 days since they married.
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".
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: As Kirby is showing Roz his prom pictures, she sees the picture with his hand on her behind. In the scene her hair on her right changes position in the following shots from on her chest, to slightly behind her shoulder, to completely behind her shoulder.
Continuity mistake: Frasier is reading the newspaper while Eddie stares at him. He picks up his coffee and we can see he's reading the back page of the newspaper, but from the angle over his shoulder he is reading the front page. It goes back to him reading the back page as he says "you will not distract me" to Eddie.
Continuity mistake: The butler and Frasier are discussing the new president of the opera board and Ferguson pours Marty a cup of coffee. In the next shot, over Marty's shoulder, we see he already has the cup in his hand, although there was no time for this to happen naturally.