Sorry about the epithet, but in the election season, I couldn't resist! The book's detractors (relatively speaking) obviously aren't "stupid", but they do miss the point---which Varian tries to explain in the preface. So let's try a different tack. Today writing a computer program to do the math used in graduate economics is an undergraduate CS project. Let's let computers do the heavy lifting, and save people for the creative work.
That's what Varian is about. What the world needs is not more people who can manipulate derivatives of implicit functions, but more people who can connect data and stylized facts to appropriate (already known) theories. That's what this book tries to teach, and it is best of breed. Although it's not clear to me that "thinking like an economist" can be taught with great effectiveness (it's a "knack", not an algorithm), Varian over and over again demonstrates that he can clearly express the "inner working" of that mode of thought. As in Information Rules, he demonstrates that he can bring these ideas to those who are not going to be professional economists, but need to understand the analysis.
Of course, some in the audience for this book will make careers in which they seek, and find, data and facts that defy existing theory. For them, of course there are better ways to prepare for the technical prerequisites for graduate school. But years later, none of those books will be nearly as much help in avoiding a dissertation proposal that crumbles into dust, too dry to support itself.
Belongs with Samuelson's classic introductory text on your bookshelf.