While shooting aerial footage over Greenland, the second unit camera crew accidentally filmed a secret U.S. military base. Their plane was forced down, and the crew was suspected of being Soviet spies.
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.
Peter Sellers was paid $1 million, 55% of the film's budget. Stanley Kubrick famously quipped "I got three for the price of six".
George C. Scott was reputedly annoyed that Stanley Kubrick was pushing him to overact for his role. While he vowed never to work with Kubrick again, Scott eventually saw this as one of his favorite performances.
Peter Sellers improvised most of his lines. And one of the most significant is in the final scene, when Sellers as Dr. Strangelove, exclaims "Mein Führer! I can walk!" According to Kubrick, "Peter said he couldn't promise to do the same thing twice. And he couldn't do anything more than two, three times. So the day we did the sequence...I had six cameras lined up and he came in and... no one knew what he was going to do, himself included."
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.