"We always talked about something going wrong with the bomb. The bomb, Dimitri, the hydrogen bomb."
I understand that Sellers was originally supposed to play 'King' Kong too, but he could not get the Texas accent right. Slim Pickens, according to rumor, did not understand much of the significance of the performance he was giving.
Anthony Harvey, who was the cinematographer, revealed that the movie was originally supposed to end with a pie fight (remember the table with deserts the Ambassador is presented with). However, because JFK was assassinated while the film was being made, either Kubrick or the studio thought it was be undignifed for the film to end with the President being involved with that. As it is, the end is kind of haphazard (Roger Ebert considers it a masterpiece but still felt the movie should have immediately cut to the final seqyence after the first bomb dropped.)
When I first watched the film I thought that the Air Force slogan 'Peace is Our Profession' was a joke by the writers. I didn't know it was actually the Air Force slogan at the time.