The briefcase carried by the priest which Frasier and Niles mistake for Frasier's, is in fact the same one Kelsey Grammer normally uses. You can tell by a pattern of stains on the side near the top. It's understandable that they would use the same one, of course, since it would be of no practical value to provide an exact duplicate for this brief scene.
When Daphne's at KACL, she sits down and picks up the headphones and uses them but in the next shot, a fraction of a second later, the headphones are on the table.
Roz: (to Niles) Everytime you see me, you have some kind of snotty remark to make.
Niles: Name one!
Roz: Well just last week, you said my bedroom was easier to get into than a community college!
Frasier: Don't stare at me, Eddie. I'm a humane man but in the mood I'm in, I could kick a kitten through an electric fan!
For his work in this episode, Nathan Lane was nominated for a 1995 Emmy for Outstanding Guest Actor in a Comedy Series.
A caller named Denise is uncredited and there is speculation that it may be Kim Basinger.
The full version of the proverb stated in the title "Fool Me Once, Shame on You, Fool Me Twice..." is Fool me once, shame on you; fool me twice, shame on me.