When filming began in the US, the stricter censorship codes of the Hays Office there were applied. One of the most obvious differences between the scenes shot in the UK and those filmed in the USA is that the tops of the actresses' costumes were buttoned up all the way to satisfy the Hays Office. That kind of clue makes it easier to identify the US-shot scenes than trying to spot differences in the sets.
Filming began in Britain, but because of the Blitz, the production relocated to Hollywood. There was such a long break in production, Sabu's early scenes had to be re-shot because he had grown several inches.
The correct spelling of the title ought to be the Thief of Baghdad, as it is a western film and this is the expected English spelling. However some of producers and Writers are of eastern European descent where the alternative Bagdad version is sometimes used. Other variations include Bughdad and Bhagdad.
The first assigned director, Ludwig Berger, wanted his old friend, 80-year-old Austrian operetta composer Oscar Straus, to compose the score. Miklós Rózsa only won the assignment by sitting in an office adjoining Berger's and playing his catchy melodies over and over. The Viennese waltzes that Straus had supplied were quickly dropped in favor of Rozsa's sweeping and colorful score.