9 minutes into it, Martin says he'll need an extension cord so he can plug in the vibrating part of his ugly old chair that just got delivered to Frasier's apartment. Over the years that chair is never plugged in and Martin never has a vibrator on. Many years into it, Frasier then tries replacing Martin's ugly old chair with a black leather one that DOES have a vibrator and massager in it, and Martin thinks that's disgusting.
When discussing the possibility of a live-in health care worker, Martin suggests the room across from his, Frasier's study for her to stay. In later episodes, Martin's room is shown to be on the same side of the apartment as Frasiers, whereas Daphne's is on the opposite side past the kitchen.
Martin tells Daphne that he had been a police officer for 30 years as of his forced retirement in 1991. Later episodes establish that Martin was already a police officer in 1952, the year Frasier was born, so Martin must have been a police officer for at least 40 years.
The time on the clock behind Roz goes from 3:50 to 3:48 in the next shot.
Frasier's program ends with the wall clock showing 10 minutes before the hour.