We think of Abbott and Costello as burlesque comics, but the medium that gave them the national exposure allowing them to go into film was radio. It was on radio that the sharpness of such routines as "Who's On First" was demonstrated to millions, laying the groundwork for the film audience that Universal benefited by. And it was WHO DONE IT? that was their film about radio. They are soda jerks in a restaurant in the building that a radio station is headquartered in. They both want to break into radio. But when they are finally on the premises of the station, they are among the witnesses (and suspects) at the murder of the station's owner (Thomas Gomez). Due to Costello's continuous ability to make errors, they are suspected of the murder by the two detectives (William Gargan and William Bendix) who are assigned to the case. They are determined to try to solve the case and clear themselves.
Gargan and Bendix were ideal foils for A & C, especially Bendix who meets Costello's dumb with dumber. The nadir for both cops is when they are guarding the front of the office building from Abbott and Costello entering it while the investigation is continuing. Bud and Lou, determined to enter the building, walk in backwards, so the cops think they are seeing them walk out (at least momentarily). Rumor has it that Costello determined never to make another film with Bendix - he was jealous of the latter's getting more laughs than him. It may be true, but then Lou was doing pretty well on his own here.
As it is a war picture, the mystery also deals with a spy ring. The actual perpetrator is a surprise of sorts at the end. A good comedy, I give it 8 out of 10.