When the B-52 is flying low over Russia, the shadow on the ground is a Boeing B-17G, a World War II propeller driven bomber.
Kubrick originally wanted to make this a serious drama. During the screenwriting process he was confronted again and again with situations that were completely truthful and serious, yet he was afraid and audience would laugh at how absurd it is. Such as general Turgeson referring to general Ripper's sending an entire bomb wing to obliterate Russia as "Overextending his authority". He eventually figured out that the only way to write it would be as a comedy.