The stories are well told, and worth listening to; Dyson is not merely a humane and vastly learned man, but a genuinely wise one. All the same, when I lay the book down, I can't help but entertain more than a few doubts. Sometimes his facts are a bit wonky (e.g., claiming that early exposure to computers causes economic inequality). Sometimes, and very surprisingly, he shows a certain lack of imagination --- considering that such a half-assed effort at administration as the Roman Empire lasted until 1453, and how much better we are at creating and maintaining formal organizations than all previous ages, it would not surprise me unduly to learn that states now in existence were still strong a thousand years from now (whereas I would be flabbergasted if, in those same thousand years, mounted nomads from central Asia had conquered sedentary states).
More importantly, I can't take his stories about the future too seriously. Partly this is because I think he, like another of his inspirations, the physicist and Communist J. D. Bernal, he relies on a false notion of human evolution. Our tools evolve so that we don't have to. Artifacts, to distort Herbert Simon's teachings just a bit, are interfaces, that must fit both sides, us and the world. So long as improving artifacts can keep up that balancing act, there is no need for us to evolve, and surely no very compelling reason. Again, that the human brain, as evolved, could be retrofitted for radiotelepathy, let alone collective memory and consciousness, seems to me supremely doubtful, and there's no reason to think it would confer any advantage over our normal sorts of memory and consciousness. (Solidarity forever is one thing, redoing humanity so as to bring a true hive mind into existence for the first time quite another.) So I think he's misconceived the way we evolve, and the mechanism driving that evolution; but there is another, perhaps even more compelling reason not believe his, or indeed any, stories about the future of science and technology and their effects. By definition, we cannot know the content of any discovery until it is made; yet it is precisely the effects of discoveries lying in the future we wish to know! (Even if we were perfect Laplacian calculators, we would need to know not just what the true laws of physics were, but that our knowledge of these laws was accurate and complete, which could never be determined on empirical grounds.) This argument against all forms of prophecy seems to have originated with Karl Popper in The Poverty of Historicism (1945) and has never, so far as I know, been refuted.
In some ways Imagined Worlds is an admirable piece of science fiction, only without the conventional fictional form; as I hinted above, SF writers have already begun to mine Dyson for ideas, as their predecessors mined Haldane and Bernal. (Fair's fair: Dyson has taken inspiration from many of the great works of SF, and also Jurassic Park.) Like the best pieces of science fiction, it enlarges the mind --- both what we think possible, what our imaginations are willing to conceive, and what we care about, the horizons within which our interests are bounded. Unlike many of the best writers of science fiction, Dyson is not in the least gloomy (something I can't help but feel has to do with his being a working scientist and not a writer). The next few years, maybe even the next century or two, might be full of trouble and decay; but over all the curve is upward, in the long run intelligence will live for ever, mutate and take over the worlds. Those who go to the prophet Dyson to learn what the future holds are, alas, wasting their time: our picture of the future turns round and round like a small wheel in the middle of Fortuna's greater wheel. But those who go to hear Uncle Freeman spin his yarns will see the dry bones of speculation rise, covered in the flesh of compassion with the breath of hope in them, and live.