As the Hats approach the crater at the restricted testing range, the brown canvas bag that had been hanging over the front of the car disappears.
During Hoover's first meeting with Gen. Timms, Hoover's cigarette disappears between shots.
It is assumed that they drove from Los Angeles to the Nevada Atomic test sites, as no atomic testing ever took place in California. Even in 2019, the one way driving time is over 4 hours. In the early 1950's, it would have been longer, and that does not take into consideration the time to go out to any of the test site entrances. The scenes where they supposedly do this, is accomplished in the daylight of a single day.
While on restricted government land, at the time the Nevada Test Site, the Hats peer into the crater from an atomic bomb shot. The crater was actually formed from the Operation Plowshare, Storax Sedan shot on July 6, 1962.
Col. Fitzgerald wears the insignia of the 31st Infantry Division on his left sleeve, denoting his current assignment. While this division was activated during the Korean War, it was comprised of National Guard units from the SE United States. They were assigned to Camp Atterbury, IN, never in Nevada or California, trained replacements, and were not involved in any atomic tests.
The Hats place their hats on Coolidge's coffin, but later Nolte has his on.
During the fight in the plane, two gunshots are heard before anyone draws a gun. Later, two muzzle flashes are visible (including the one that punctures the cockpit), but no sound effects accompany them.
Prior to Hoover and Coolidge boarding the C-47, the underside of the port wing is shown. Civilian registration numbers can be seen through the paint. This particular aircraft is a civilian DC-3 that has been painted over in US Air Force markings.
At about an hour and ten minutes into the film, Melanie Griffith's character has a pack of cigarettes on the table in front of her. The brand is Tareyton, which wasn't introduced until 1954. While activity was definitely happening at test site in 1954, the film is staged more for the early part of the decade. If it was 1954 or later, after the brand was introduced, the packaging would have been different with the name "Herbert Tareyton" printed across the top half and no vertical red stripes.
When Hoover and his men are caught trespassing by Colonel Fitzgerald and the MP's, there is an offstage ADR line heard as one of the men speak on the radio, "Sierra, Tango, Zero, One." "Sierra, Tango" is the phonetic alphabet representing the letters "S" and "T". However, this is the current phonetic alphabet which became effective in 1957. The ADR line should have read, "Sugar, Tare, Zero, One" to be authentic to the period.
Where the four detectives are trespassing on the military area in the desert the paved road they are on driving on has a double YELLOW center line. Yellow was not used in the USA until 1971.
In opening scene of Jennifer Connelly's boudoir, she is shown smoking a 100mm cigarette. Other characters, including Nick Nolte, smoke similar cigarettes throughout. The first such cigarette in 100 mm length was introduced only later, in 1966, by R.J. Reynolds. Until 1966, "King Size" (roughly 80-85 mm) was the longest cigarette available.
When Nolte's character first meets McCarthy's character there is a man appearing and disappearing behind the dune behind McCarthy.