Other mistake: When Frasier enters the apartment, Martin and Sherry are talking in the kitchen. If you listen carefully to what they're saying, their conversation makes no sense. Martin says something along the lines of "Daphne is really a very nice girl" before suddenly, in a very different tone of voice, he says "You're right, we're not getting enough privacy around here". Seems like a big chunk of conversation was edited out.
Other mistake: Clive called the condo to ask for Daphne. Later, when he is under the impression that Daphne is married to Niles, he says that Daphne is still listed in the phone book as Daphne Moon. Why is Daphne listed under Frasier's home number? The episode "Dial M for Martin" establishes that she feels a need to move on when a patient no longer needs her. At this point, she does not consider herself a permanent part of the household.