While shooting aerial footage over Greenland, the second unit camera crew accidentally filmed a secret US military base. Their plane was forced down, and the crew was suspected of being Soviet spies.
Peter Sellers was paid $1 million, 55% of the film's budget. Stanley Kubrick famously quipped "I got three for the price of six".
The scene where Gen. Turgidson trips and falls in the War Room, and then gets back up and resumes talking as if nothing happened, really was an accident. Stanley Kubrick mistakenly thought that it was George C. Scott really in character, so he left it in the film.
The film led to actual changes in policy to ensure that the events depicted could never really occur in real life.
In the early 1960s the B-52 was cutting-edge technology. Access to it was a matter of national security. The Pentagon refused to lend any support to the film after they read the script. Set designers reconstructed the B-52 bomber's cockpit from a single photograph that appeared in a British flying magazine. When some American Air Force personnel were invited to view the movie's B-52 cockpit, they said it was a perfect copy. Stanley Kubrick feared that Sir Ken Adam's production design team had used illegal methods and could be investigated by the FBI.
Stanley Kubrick: [bathroom] Gen. Turgidson's first scene and Gen. Ripper's final scene take place in bathrooms.
Stanley Kubrick: [Maniacal staring face] Gen. Jack D. Ripper explaining his plot to Group Captain Mandrake.