President John F. Kennedy very frequently set up recording machines during meetings at the White House. Much of the dialogue from the movie is taken directly from Kennedy's tapes.
The fact that John F. Kennedy agreed to secretly remove US missiles from Italy and Turkey did not become public knowledge until many years later.
In Boston, Kevin Costner's attempt at a Boston accent is so notorious that a "Kevin Costner accent" is an accepted slang term for a non-Bostonian's unsuccessful attempt at a Boston accent.
The pilots of the RF-8 Crusader which were shot at by the Cubans were played by actors with a connection to the real people involved - David O'Donnell, who plays Lt. Bruce Wilhemy, is the real-life grandson of Kenny O'Donnell, while Christopher Lawford, who plays Cmdr. William B. Ecker, is the real-life nephew of President Kennedy & Robert Kennedy.
On February 1, 2001, this was the first film to be screened at the White House by President George W. Bush and Laura Bush. In attendance at the historic screening were members of the Kennedy family, members of Congress and personal friends of the President and First Lady.