There's no way to pinpoint exactly where the moonwalk came from, as dances tend to evolve and build upon previous ones. However, the earliest footage of someone performing a sliding, backward dance step that looks something like the moonwalk comes from the 1930s short films of Cab Calloway, a jazz and big bandleader. Calloway called it "The Buzz," but it was jerkier than and not as floaty as the modern moonwalk. There was also a popular ragtime dance in the same era called "The Camel Walk," which is a forward, zigzag dance step that also requires the dancer to drag his feet. Tap dancer Bill Bailey's sliding backstep in 1955, however, was really the first to truly look like what we think of as the moonwalk.
So where does mime come in? There's a stationary version of the same kind of gliding step that is commonly used in mime, most notably by Marcel Marceau in his famous "Walking Against the Wind" routine first done in the 1930s, known as the airwalk. Mime artist and actor Jean-Louis Barrault performed the airwalk in the 1945 film "Les Enfants du Paradis." Shields and Yarnell, an American mime duo in the 1970s who briefly had their own variety show, also incorporated the airwalk into their repertoire. Mime influenced dance styles like popping.
Popping (see sidebar) also evolved in this decade and was shown to a national audience on dance shows like "Soul Train" and, in the early 1980s, on "Solid Gold." Dancer and singer Jeffrey Daniel probably has the distinction, along with fellow "Solid Gold" dancers Geron "Casper" Candidate and Derek "Cooley" Jaxson, of bringing the backslide (now actually called by that name) to a new generation in the 1980s. Daniel did the moonwalk as part of a routine on the British show "Top of the Pops" in 1982 (which also incorporated many mime movements) and astounded the audience there. Many people believed that the dance floor must've been oiled, or perhaps that Daniel was wearing wheeled shoes or being pulled by an invisible line, in order for him to glide so smoothly.
Next up, how Daniel, Casper and Cooley all taught Michael Jackson the moonwalk ... sort of.