The July 1, 1952 issue of Look magazine did not have Eisenhower on the cover as depicted, but a group of six pictures. One was of an Air Force fighter plane with the same blurb as the film's magazine: 'Flying Saucers - The Hunt Goes On'.
The April 7 1952 issue of Life Magazine had Marilyn Monroe on the cover, not Harry Truman. It was her first magazine cover. It was the U.F.O. issue though, with the blurb for it in the upper right corner, as shown in the film.