Jackie Gleason released a version of the title music as a single on Capitol in early 1964, with another Henry Mancini composition, Bird Brain, as the b-side. This puts Soldier in the Rain (1963) in the same category as Thunder Road (1958) and Because They're Young (1960): movies which had a version of the theme song performed by a member of the cast and released as a single, while that version wasn't the one used in the movie.
The camera Clay uses for the "pin-up" contest is a Polaroid Land Camera Model J66. It uses Type 47 black and white roll film and was manufactured between 1961 and 1963. Retail price was $89.50 (or about $700 in 2016).
The large patch on the left shoulder of everyone's uniform is of the U.S. Sixth Army. At the time of this film, it was headquartered at The Presidio in San Francisco. It was the training Army for soldiers being sent overseas. Inactivated in 1995, it was reactivated in 2008 and is now headquartered at Fort Sam Houston in Texas.