When Daphne first enters the apartment, she walks into the kitchen to retrieve a coffee mug. She then returns to the dining area and places it on the table. The camera angle changes and she is seen placing the mug on the table a second time.
The level of coffee in the pot on the table changes several times throughout the scene.
Niles tells Martin that he shouldn't drive to Rattlesnake Ridge because it's 5 hours away. In actuality, it's only about 30 minutes from Seattle.
Daphne (Jane Leeves says that Clive (Scott Atkinson) is her ex-fiance. However, in Season 1's Death Becomes Him (1993), Daphne explains to Niles (David Hyde Pierce) in great detail that she had never had a serious boyfriend.
When speaking to the caller "Keith", Frasier mispronounces "narcoleptic" as "narcolectic". A psychiatrist would know how to pronounce the term correctly, never mind Frasier's noted pomposity when it comes to speaking correctly.