Fred Astaire had been set for the lead for this film since the mid-1940s by producer Arthur Freed. The film was originated as a project for Astaire and Judy Garland. But since the two stars had overlapping film schedules, the project never materialized until the early 1950's with Astaire and Vera-Ellen.
There are two versions of Fred Astaire's "I Wanna be a Dancin Man" number. The first was shot in front of a red curtain in a more casual attire. Other than that it had the exact same choreography. MGM wasn't pleased with the costume, so they reshot the number in front of a different backdrop, with Astaire in a far more debonair suit. When they made "That's Entertainment III" they did a split screen comparison of the two numbers.
The song "Baby Doll" was composed by Harry Warren/Johnny Mercer for "Take Me Out to the Ball Game" but deleted before release. The DVD special features of that film include part of the number sung by Gene Kelly and danced by Kelly and Esther Williams. The new version sung by Fred Astaire and danced by Astaire and Vera-Ellen is exactly the same, with lyrics by Betty Comden and Adolph Green.
The "walking/dancing on air" SPFX were done with a traveling matte. This is especially evident when Fred Astaire is dancing alone near the top of the monument. His cigarette smoke is visible only so long as it is over his body, vanishing immediately as it moves to the side.