Well *after* Al is told about a December 1952 flap that turned out to be the planet Jupiter, the story turns to events it states are happening in July 1952.
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 shown prominently in the movie has President Truman on the cover. In reality, actress Marilyn Monroe was on the cover.
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.
In a recreated scene supposedly taking place in January 1948, the wall calendar in the background is actually for January 1955.
A watch seen in a closeup during a recreated 1948 scene is a 1953 model.
When a stack of recreated 1952 Life Magazine issues is shown in a close-up, a stack of another magazine's real issue from 1955 is next to it.
When Chop is going over a report on solved vs. unsolved UFO sightings, a moving shadow of the boom microphone is visible on the wall map behind him.
When Chop is asked for his full name when applying for the Public Information Office jog at Wright-Patterson, he says "Albert M. Chop", not saying what the "M." stands for.