Factual error: One of the scenes shows the buildup of American readiness as tensions mount. A B-52 bomber appears carrying four white menacing-looking missiles under her wings. Such missiles can easily be identified as the Hound Dog type, which was under test in the mid-60s but never became operational. America would never deploy those missiles either for real or for training, because the project was scrapped before even being accepted into the Air Force.
Factual error: The U-2 was built to fly on the edges of its flight envelope: too slow yet too high. The pilot had a very difficult time keeping it level and straight so it wouldn't stall. In the film, a U-2 evades missiles by jinking up and down as if it were a fighter, until a final missile strikes it down. That aircraft would never have been able to even climb away from the first missile, all it could do was sit and wait for hell to reach up. Those aerobatics were completely out of the question for a U-2.
Factual error: On the scene where the 2 low-flying RF-8 Crusaders are being shot at, the Cubans and Russians are aiming what supposed to be a mobile SAM launcher, that resembles SA-3. As far as I know, at the time the Soviets had no mobile SAM, until the introduction of the SA-6 in 1966.
Factual error: In the last scene in the film, Costner and his family are seen having breakfast before going to mass. The problem is, they are portrayed as a strict Roman Catholic family. No strict Roman Catholic family would eat breakfast before going to mass at that time. In 1963 you were not even allowed a glass of water from the moment you woke up till you took communion at mass.
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!
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."