Books that combine an excellent review of quantum physics with a provocative world view should probably merit a baseline three stars, and this one does. That said, The Beginning of Infinity does not seem to have the makings of a classic in the genre.
As numerous reviews have pointed out, this book is a David Deutsch "Theory of Everything", not in terms of uniting all four of the basic forces of physics (though in a sense he does that), but in the sense of expanding quantum physics into a theory that encompasses everything that we humans tend to hold meaningful. Thus the book includes attempts to show that an absolute standard of beauty, a system of ethics, and even systems of politics and (loosely interpreted) parenting and education can be derived from Deutsch's unique point of view.
In The Beginning of Infinity, Deutsch goes to great creative lengths in an attempt to make quantum physics less mysterious and more comprehensible. In this he succeeds better than many other authors. As an educated person that has made an effort to keep up over the last five decades with advances in science, but still regularly gets pushed into "I'm FAIRLY sure I understand what is being said" territory, I found Deutsch's explanations illuminating and very helpful. Deutsch's explorations of the implications of the well-known single photon studies (leading many, but not Deutsch, to say that photons are "both particles and waves") are striking and deeply exciting. Deutsch is an acknowledged leader in quantum theory and quantum computing, and when he discusses topics that he knows best, he seems to be on the most solid ground (as solid as anything can be in this quantum world!). It is when he strays from his area of expertise that he begins to take on the colorations of many other great scientists that wander off into clouds of quirkiness when they leave their area of expertise. Linus Pauling on Vitamin C, James Watson on race, Lynn Margulis on the cause of AIDS come to mind.
When Deutsch jumps with all four limbs into philosophy, anthropology, politics, and education, he does so with a maximum of enthusiasm, and not a little combativeness. Often defending his positions by preemptively consigning any and all opponents to an "ism" (e.g. empiricism, reductionism, rationalism, "isms" ad infinitum), Deutsch's arguments vary wildly between seeming shockingly superficial and too profound to easily grasp. It is instructive, if you have the time, to watch the TED lecture (YouTube) that Deutsch gave in 2005: it gives a sense of just how static his points of view have remained over nearly a decade.
When Deutsch discusses Artificial Intelligence, he seems woefully out of touch with the literature that has emerged over the last five to seven years. When he discusses why mankind is a species of animal that is different in kind, rather than degree, he ignores (and is often factually incorrect) when citing animal research data regarding non-human language capabilities and levels of consciousness. When he describes humans as "universal constructors" and/or "universal explainers" (i.e. capable of infinite progress in both related arenas) his arguments often, again, seem out of touch with current research on neuroanatomy, consciousness, and far more in synch with the powerful drive we humans have to think of ourselves as unique in all the universe.
Deutsch's estimation of the human mind's infinite capacity requires him to climb further and further out on epistemological limbs. If one could compare Deutsch's science of the human brain to the field of astronomy, it would be fair to say that he runs a very significant risk of being a Pre-Copernican: it's probably just not true that EVERYTHING with advanced computational capacity revolves around the human mind, now and forever.
Deutsch diverges almost imperceptibly, but very significantly, from much contemporary evolutionary/complexity/emergence theory when he uses the word "knowledge" in place of the word "information". Whereas a fair amount of contemporary thought has been devoted to the emergent phenomena that occur as more and more information (down to and including the color and spin of quarks) coalesces in a process that started with whatever we think the Big Bang may have been, by using the word knowledge instead of information, Deutsch appears to coopt the evolution of information by establishing human ownership of it. If information, starting in its most basic form (quarks? Superstrings?) evolves in increasingly complex ways over the life of the multiverse, then humans are simply a particular (in this case, primate) manifestation of an inevitable process that is independent of humans. An evolutionary process that is akin, then, to what Kevin Kelly seems to allude to in his striking book What Technology Wants. If on the other hand, "knowledge" is the key evolutionary factor, then humans (who translate information into knowledge and are the sole possesors of knowledge) are absolutely necessary for forward motion. Motion toward infinity, Deutsch proposes, needs the current version of Homo sapiens (Deutsch distinguishes between current and past versions). Which is an attractive proposal to me from an egotistical point of view, I'll admit. But then....I read the morning paper. And it makes me hope that the Multiverse, in all its Information, has more in store for the future than Mankind Uber Alles.