When the narrator talks about Vasili Arkhipov being the Russian officer who cast the single vote that prevented a Soviet nuclear strike during the Cuban Missle Crisis (and possibly preventing WWIII), the narrator refers to Arkhipov as the "Political Officer" when in reality he was a Naval Officer and second-in-command.
When the narrator talks about 'a U2 spy plane' for the first time in the introduction to the Cuban missile crisis, the plane depicted in the sequence is actually a Boeing B-47 Stratojet, which is a nuclear bomber, not a high-flying reconnaissance aircraft.
When the narrator speaks of the "50 plus Megatons" Soviet nuclear test, the actual shot in the sequence shown is NOT that test but the American 'Crossroads Baker' shot of 1946, 15 years earlier, which had a yield of only 21 kilotons, which is 2,380 times smaller.