While it is obvious that the group of reporters at the press conference at the end of the film contains both male and female reporters (and he even takes a question from a female reporter), the president repeatedly refers to them as "gentlemen".
When Paul Girard visits Admiral Barnswell on his ship at Gibraltar, he arrives in full daylight and demands the admiral's statement immediately. When he returns to shore it is fully dark. Since his business is urgent, this must not be long after sunset, and hence in Washington it should still be afternoon. Yet at the same time, Ellie is cooking dinner there.
At the end of the meeting convened by the President in which Colonel Casey, Senator Clark and others are arguing whether or not the plot is real, the pictures on the right end of the mantel in front of which Colonel Casey is standing change several times.
When the president's secretary, reporting Paul Girard's death, tells Secretary Todd that the plane's wreckage is scattered for miles, she is seen moving her arms to her sides twice - as the president is shown leaving the room, then again immediately after as he's shown entering the side room.
When Senator Clark is driving in the desert outside of El Paso looking for the "ECOMCON" base, in a medium shot he can be seen with his left arm hanging outside the vehicle, resting against the driver's door. When the car stops and Clark looks around, a close-up shows him to have both arms inside the car and both hands on the steering wheel. The next shot is a medium shot as he begins to drive off and his arm is again hanging outside the car, resting against the door.
When "Jiggs" and the FBI man are following someone down a dark alley into a parking garage, you correctly see "Jiggs" shadows grow larger as they walk toward the end of the alley, but when the 2 men turn the corner, there is another man's shadow there which moves just slightly.
Jiggs and Senator Clark are at Dulles Airport in Virginia. Jiggs leaves the airport and there are palm trees outside. It looks like the outside of LAX, not Dulles. Moments later Jiggs and the Secret Service agent are driving down the National Mall towards the Capitol Building, which is twenty-five miles from Dulles by road.
When Pres. Lyman tells Gen. Scott "All you have to do is wait a year and nine months for something called an election", he has the time frame wrong. One year and nine months from May would be February. He should have said "Wait a year and six months", which would have placed it in November, the correct month of the next election.
Site Y appears to be staffed by units of US Army Special Forces. The patch worn on the Green Beret is known as a flash, which is in the shape of a shield, and identifies the individual Special Forces Group. It is mistakenly worn upside down in the film. All Special Forces officers in the movie are wearing the Special Forces Crest on their flashes. Only enlisted personnel wear the crest on the flash, officers wear their rank.
General Scott is wearing his Medal of Honor (MOH) ribbon over the right pocket of his uniform coat. The MOH ribbon is never worn in that location. It is supposed to be worn along with the recipient's other ribbons above the left pocket (in the topmost position).
While briefing General Scott on the previous All Red alert exercise, Colonel Casey refers to Wright-Patterson Air Force Base as "Wright Field." The latter name was used only until 1947, at which time the base was renamed W-PAFB.
Several officers, including General Scott and Colonel Casey, sometimes wear their service hats or overseas caps indoors. This violates military custom, which requires headgear to be removed while indoors except while participating in ceremonies.
All the ECOMCON officers and enlisted men at the top secret Site Y base are wearing unit insignia and badges on their fatigue uniforms. But troops participating in an actual top secret operation like this one would be wearing "sanitized" uniforms (no insignia).
In many scenes, members of the Army and Marine Corps are wearing their summer uniforms but General Scott and other members of the Air Force are not. They should be wearing their summer silver tan uniforms which were the summer uniforms of that era.
When Harold McPherson introduces Gen. Scott for his speech at the American Veterans Order convention in New York, he says that Scott is "the winner of the Congressional Medal of Honor and two Distinguished Service Crosses". However several closeups of the ribbons on Gen. Scott's blouse seen during the film do not support this statement. The highest decoration among his ribbons is for the DSC, not the Congressional Medal of Honor for which he is not wearing a ribbon at all. Scott's DSC ribbon also does not have a device attached to it to indicate a second award that Mr. McPherson said he had won. Scott's DSC, which is only awarded to members of the Army (including the Army Air Force), would have been won by him during WWII as opposed to the Korean War (he wears campaign ribbons indicating service in both conflicts) as it was no longer awarded to Air Force personnel after 1947 when the Air Force became a separate service. (The Navy and Marine Corps equivalent award is the Navy Cross and after 1947 the Air Force became the Air Force Cross.)
At the time of this movie, there were five nuclear powers: USA, USSR, UK, France, and China (China only became one in 1964, the year of the movie but the film is set in the near future from 1964).
However, the treaty only speaks to disarmament between the US and USSR. The other three are not mentioned. The UK and France depend on their nuclear arsenals to counter the USSR's close and massive superiority in conventional forces. Also, by 1964, the relationship between China and the USSR had deteriorated dramatically to the point they shared the world's longest armed border.
In the scene at Blue Lake (the Presidential retreat), we see a hidden Secret Service motion picture camera that is supposedly recording the movements of a suspicious motorboat offshore. But the camera is aimed nowhere near the boat.
In the Blue Lake scene, the placard describing the Secret Service's filming of the boat shows the time to be 0615 hours (6:15 a.m.), yet the bright sunlight indicates it is actually much later in the day.
The placard the Secret Service agent holds in front of the hidden camera at Blue Lake contains the day of the month but not the year the filming was done, a crucial error if they had later to establish the film's provenance (Broderick could claim it was shot some other time).