The film is not a documentary. Rather, it is a dramatization. Compressing Thirteen Days into 145 minutes necessitates distortion of many specific historical facts. But the central themes of the movie and the principal takeaways are essentially faithful to what happened when JFK and Khrushchev stood eyeball to eyeball in 1962...
Thirteen Days dramatization gets a number of specific historical facts wrong:
inflating ODonnells role to that of elder brother of President Kennedy stiffening the presidents spine, on the one hand, while corralling military leaders bent on war, on the other;
caricaturing the military leadership as a war-mongering monolith;
miniaturizing most of the other advisors, particularly Bundy, Sorenson, and Dillon.
In what Charles Krauthammer has called an ideological lie, the movie portrays military leaders seeking to maneuver the President into war. The image of Kevin Costner, as Kenny ODonnell, calling pilots flying over Cuba to persuade them to lie to the chain of command for the larger good of the country is unreal.
The more important question, however, concerns the films central messages. How faithful is the movie to the central truths about this historical event? Here, I believe, the producers deserve high marks. They have not only attempted, but succeeded in entertaining in ways that convey messages that resonate with the central truths of the crisis.