Fred Astaire's character explains what causes war in this video clip. There are 7 short clips (ranging from 1 to 8 minutes long) from the 1959 version of this film at googlevideo. The segment showing the car race is here. A clip from late in the film is here. Another late scene with Anthony Perkins is here.
TCM has an overview. 1000 Misspent Hours calls it "a memorably affecting film" but adds
The more serious problem is that Kramer loses all capacity for subtlety whenever he reaches a scene that bears directly on what he really wants to say, leading him to begin piling on jarring camera maneuvers and obnoxious musical stings.
Moria says "On the Beach’s distinction is not really that it is a very good film, merely that it was the first." and
The pace also drags hideously. The reason for this is that Stanley Kramer deems it necessary to spell every issue out in bold several times over. He leaves nothing understated. The film literally talks us to the end of the world. And not merely content with portraying the end in a grim light, Kramer at the end turns and directly preaches to the audience, allowing, with an appallingly heavy-handedness, the film to fade out on the image of a Salvation Army banner, “There is Still Time ... Brother” sitting in the midst of a city empty of all human life.
The New York Times Review doesn't mind the preachiness, saying
In putting this fanciful but arresting story of Mr. Shute on the screen, Mr. Kramer and his assistants have most forcibly emphasized this point: life is a beautiful treasure and man should do all he can to save it from annihilation, while there is still time.
The great merit of this picture, aside from its entertaining qualities, is the fact that it carries a passionate conviction that man is worth saving, after all.
The 2000 made-for-tv remake is divided into 20 pieces at youtube. Part 4 is missing. Part 5 does not follow directly from part 3, so there does appear to be a section unaccounted for. Part 1:
part 2, part 3, (no part 4 listed at youtube), part 5, part 6, part 7, part 8, part 9, part 10, part 11, part 12, part 13, part 14, part 15, part 16, part 17, part 18, part 19, part 20
The book is wonderful (though I have to make an effort to look past the blatant 1950's sexism).