The "On the Air" sign is still on after Kenny cuts the mike in the announcer's booth.
When Mr. Martin (Miguel Sandoval) exits his office in the Black Tower, someone's hand can briefly be seen grabbing hold of the door after he opens it.
Normally, people entering Frasier's apartment come from the elevator directly across from it. But when Martin and Daphne return from the police station, Daphne enters from the side, presumably for more dramatic effect.
Frasier refers to Polynesia and Scandinavia as countries. They are regions; it's highly out of character for a pedant like Frasier to make such a slip.