Lost in a Harem (1944)

A trio of performers get in trouble with the law and are helped to escape under the condition that they will help a dethroned prince from a mythical Arabian Nights desert kingdom defeat his wicked usurping uncle.

Featuring a giant; a mind reader; a pair of magical Cat's Eye rings, (Abbot and Costello get hypnotized into thinking they are termites, and they eat some palace furniture); plus, a talking skeleton in a dungeon which leads into 'Mike's', a phantom bar with interaction with invisible furniture, sound effects and all. The last one was a gag was reused on their TV show; and which for some strange reason is somewhat reprised at the conclusion of Michelangelo Antonioni's 1966 film Blowup.

Nice camera work, (especially during the musical sequences, whatd'ya expect, this is an MGM after all! These interludes aren't just interruptions, they are the show), overall good production values with cool forced perspective sets and excellently matched matte paintings.
A careful bit of casting (Douglass Dumbrille and Lottie Harrison whose likenesses are immediately obvious,) allows the filmmakers to get away with the old mirror gag.

Bud and Lou supported better romantic 'leads' than most other comedians were forced to. MGM formula works well for a comedy team: Comedy, Romance and Musical elements are all nicely balanced for once,

With Marilyn Maxwell, John Conte and a redubbed Lock Martin.