Other mistake: The guy who plays Clive in this episode has one of the most appalling accents I have heard. He's apparently from Manchester, but sounds like a sort of cockney South African. His accent slips around all the time; it's very poor. I wouldn't normally submit it, but his is so shockingly bad I doubt anyone would be fooled into thinking he was British.
Suggested correction: I think this may have been deliberate. The episode is almost meant to be ridiculous, with the characters quickly churning out lies on the spur of the moment, and everyone supporting the fake family story without objection.
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.
To Kill a Talking Bird - S4-E14
Other mistake: It seems very out of character for Niles, who is so obsessed with cleanliness, to be happy with having a bird flying loose in his kitchen.