For one thing, I do not share Greene’s enthusiasm for string theory. No matter how elegant the various forms of string theory may seem to the physicist, the simple fact is that there is no experimental proof for any of it nor is any forthcoming at our present level of technology. In fact, to the best of my (limited) knowledge, I am not sure that string theory offers any testable predictions or explanations of physical phenomena that cannot also e explained with other theories.
Brian Greene generally does a good job of explaining but parts of The Elegant Universe were a little difficult to get through, probably more because of the extreme opaqueness of the subject, and not to any lack of skill of the author. The last several chapters, however, seemed to be increasingly esoteric as Greene used string theory to explore such subjects as the interiors of black holes and the very beginning if the universe, and before.
Overall, I would recommend this book, but not wholeheartedly.