The title is based on a "mondegreen" (a misheard, spoonerized, or comically misinterpreted phrase from a song or poem): the title is from the lyric "all of the other reindeer" from "Rudolph, the Red-Nosed Reindeer". Other character names are similarly derived: the name "Richard Stands" is a malapropriation of the phrase "which it stands" in the U.S. Pledge of Allegiance, and the character name "Round John Virgin" is taken from the phrase "round yon virgin" from "Silent Night".
The reference "You sir, are no reindeer" is a reference to the 1988 Presidential debate comment made by Loyld Bentsen to Dan Quayle. "Senator, I served with Jack Kennedy. I knew Jack Kennedy. Jack Kennedy was a friend of mine. Senator, you're no Jack Kennedy".
Dan Castellaneta (the Postman) is well known as the voice of Homer Simpson on The Simpsons (1989); executive producer Matt Groening is the creator of The Simpsons; the falling letters are all addressed to Bart Simpson.
The trivia item below may give away important plot points.
Trapped in the postman's truck, Olive finds a package addressed to her containing a metal file she uses to escape. The package's return address indicates that it's from "Deus Ex Machina" (Latin for "God out of the machine"), a literary term for a contrived plot device which conveniently resolves an otherwise insurmountable problem.