Factual error: During the film, actual news footage of the Soviet merchant ships carrying missiles to Cuba are added to new scenes of alleged "Soviet" merchant ships. Whenever one of these new ships appears, it is clear that it is empty. The ships are riding so high in the water that the red paint on their hulls (normally under the waterline when the ship is fully loaded)is visible. This indicates that these ships are not carrying anything, rather than the film's implication that they are loaded with missiles for Cuba.
Factual error: Briefly, we see an Air Force ground crew loading weapons onto a fighter (the shot is approximately a second long). The fighter is a Northrop F-5, which 1) was never flown by the Air Force as a combat plane, and 2) had yet to fly for the first time in October 1962!
Continuity mistake: When they show the Cubans building the missile base they show an "army" military truck, a mid 80s Kenworth, not an early 60s.
Continuity mistake: When the US warship fires its guns at the freighter, you can see how the crew loads the guns. They load up blue grenades with white letters - blue rounds are training rounds.
Continuity mistake: When O'Donnell drives Robert Kennedy to meet with the Russian Ambassador to avert WW III, the exterior of the car changes from rain-soaked to bone dry several times during the drive.
Factual error: When Kennedy is being shown how far the Soviet MRBMs could reach from Cuba, the South American country of Colombia is spelled "Columbia."