It was a time of tremendous advancements in almost "magical" technology. Consider that 50 years prior (1900) few people had cars, phones, and radios and powered flight, television, and motion pictures were in their infancy. In the 1950's man went into space, broke the sound barrier, could travel to nearly any point on earth via flight in a matter of days (vs weeks or months just 50 years before), and communication/media/cinema were modernizing at an impressive rate.

There was a sense that anything was possible, but also a desire to predict the next big thing. Flying cars seemed logical step as did moon colonies, but also things like nuclear war and 1984.

I'm a fan of this "classical" era of science fiction and also did some research into some of the scientific culture of the time, particularly the early days of NASA. It seems amazing to me given the context of the era that such ground break ideas and such optimism for the progress of science that these people had. Particularly considering that many of them were born or grew up during the Great Depression when the "modern era" appeared to be on the brink of collapse. Modern Science Fiction just doesn't seem to offer as radical scientific ideas (compared to contemporary scientific achievements) as the things written in the '50s.

Of course a lot of this is my opinion based on a rather lengthy (but far from complete) reading list of Science Fiction, History papers/books, and some original research.