I repeat look into the National Geographic Series "Seconds From Disaster" See above for link.

Mondo Cane - Beautiful film, I think it's black and white, almost wordless, great soundtrack.

Fail Safe - The original 60's Movie with Henry Fonda or the live televised version from the late 90's with George Clooney. An error sends an american bomber out to vaporize Moscow. Not played for laughs like Strangelove, which is also a great film.

War Games - Cute but probably too stupid to show to kids these days.

There was an incredible 'modernized' version of "A Christmas Carol" showing a nuclear future written by Rod Serling and shown in the 60's.

Seven Days in May - General Burt Lancaster plans to usurp a chickenshit American President. Will his best friend Kirk Douglas betray him or America? Only Ava Gardner knows.

Hitchiker's Guide to the Galaxy. Original BBC Radio Workshop version: The end of the Planet Earth and the happy-go-lucky days which follow.

Orwell's 1984 depicts a possible future that could be thought of as a disaster. Notion of anti-utopia or dystopia. Related to Aldous Huxley's "Brave New World" or the seminal "We" by Zamyatin.

The Day After Trinity - Very Talky. Intriguing for people like me who are fascinated with the development of The Bomb.

BBC did a wonderful series called "Oppenheimer" starring Sam Waterston in one of his greatest performances. I don't know where to find it unfortunately.