Factual error: In the scene where Dave is playing cards with soldiers, some of the paper money being gambled is a design of U.S. money not introduced until about 30 years later.
Factual error: When Alma and Whit drive along the coast, the road has recessed center line reflectors. These hadn't been invented yet in 1959 when the movie takes place.
Continuity mistake: The German and British airmen are looking at the Northern lights. From the rear the men are apart, but the front shots of them show them much closer to each other.
Character mistake: It's said in the movie a vice presidential candidate never gave a concession speech. Geraldine Ferraro did this in 1984.