At the end of this episode the last shot confirms that Frasier's building has 21 floors, that Martin's room does sit next to the balcony on the right side, and Daphne's window looks out across the balcony on the other side.
The celebrity callers in this episode. Kieran Culkin as Jimmy, who calls in claiming his parents are stupid and asks how long it'll last. And Christopher Durang, who plays Rudy, who tells on air the plot of a sad movie while crying.
Pauley Perrette plays a coffee shop waitress named Rebecca. She has one line of dialogue, and her character's name is never mentioned.
The episode title is that of the song "The Impossible Dream," composed by Mitch Leigh with lyrics written by Joe Darion and written for the 1965 musical "Man of La Mancha." The song originally performed by Richard Kiley was a hit for many other singers in the 1960's. The original stage production opened at the ANTA Washington Square theater in New York City on 22 November 1965, moved to Broadway after a short run, and eventually had a total of 2329 performances. "Man of La Mancha" won the 1966 Tony Awards for the Best Musical and Best Score.
Sigmund Freud shows up at the end of this episode. In season 9's "Room Full of Heroes," Frasier dresses up as Freud for his Halloween party.