Although most of Akira Ifukube's score is replaced in the American version, if you listen closely enough you can her a version of what would become Rodan's theme in the Godzilla films from the 1960s.
The American scenes were shot in Bronson Canyon just outside of Los Angeles. Interestingly, this somewhat bothered Myron Healey who thought he was going to shoot his scenes in Japan like Raymond Burr supposedly had for Godzilla: King of the Monsters! (1956). Interestingly, when Healy appeared on an episode of Perry Mason (1957) he talked to Burr about it and Burr admitted that all his scenes were shot on a soundstage in Hollywood.
This film was so heavily altered from it's original version that merely 15 minutes of the original Japanese version remain. The stars of the original Japanese version, Kozo Nomura and Ayumi Sonoda, are only briefly seen as "Paul and Shidori Isoh." Koreya Senda's part has been completely removed.
This was originally supposed to be a co-production between ABC and Toho. However, ABC backed out just before production began.
In the Americanized version from 1962, even though the film is called "Varan the Unbelievable", the monster is called "Obake" throughout the film for some reason.