Factual error: There is a scene where interceptors, flying out of an Alaskan air base, are ordered to go to afterburners in a desperate attempt to catch the lone bomber. When the commander of the flight signals his wing to light their afterburners, they cut to a shot of a jet firing missiles.
Other mistake: The president's translator puts on his headphones just before the receptionist announces the Russians are on the line.
Suggested correction: He hears the buzzer before the receptionist speaks. Not a mistake.
Factual error: Near the end we're shown various locations of normal activity in New York City including a movie theater showing "My Fair Lady." In 1964 theatres would be single screen, and we see the marquee and box office listing showtimes. With intermission, the film runs approximately 3 hours but the showtimes listed are less than 3 hours apart.
Factual error: The B-58 bomber had a range of 1700 miles. The route they took over the USSR was over 6000 miles. No tankers were indicated on the wall map. No way they could have made it. Also, their maximum payload was two 1 megaton bombs, not 20 megaton bombs.
Factual error: Near the end of the film Colonel Cascio calls his mom in NYC to tell her to get out. However, there is absolutely no way they let someone inside the control room contact the outside world at this point giving out warnings or sensitive information about the situation. Any contact with the outside world is cut.
Factual error: When Moscow launches their anti-air missiles, the missiles shown are U.S. Nike Zeus, Hercules, or Ajax design. (01:07:00)