Continuity: In all President Kennedy White House shots, you can see the boom mike peak down several times. Look for the group shots, and the boom will be there.

Continuity: On the Pentagon the plot shows the USS John R Pierce intercepting the two Soviet ship but the marker on the plot says DD722 (it is upside down). DD722 was the USS Barton whilst the Pierce is correctly shown in the external shots as DD753.

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.

Continuity: The Pierce fires its guns to clear the barrels of the already loaded starshell. This is technically correct but when the starshells burst there are four of them i.e. the same as the number of gun barrels on the Pierce. Earlier however, when the Pierce first confronts the Grozny, there is a shot in the 5in gun turret showing at least one barrel being loaded with practice shell (i.e. solid shot). The Captain reports to the Admiral that the guns are loaded.