First, the plusses. The book reads easily, and Gleick is careful to explain all the concepts he introduces so that a layman reader will understand. There is a lot of history in this book, where Gleick first explains the person who made the discovery before he explains the discovery itself. These sections can be tedious to a reader interested in the science, not Edward Lorenz' personal habits, but it works well to steady the pace of the book, and to give the non-scientific reader a breather before diving into more scientific concepts.
You can't always have the best of both worlds, though, and so at times, a more scientifically or mathematically reader will be frustrated with the lack of detail concerning some of the interesting concepts developed here. For example, Gleick mentions fractional dimensionality, but fails to really explain it well, probably assuming that it is beyond most of his readers. This is probably a safe bet for layman readers, but left me very frustrated in places. Also, Gleick's writing (praised as "novelistic") gets overly melodramatic in places, and the reader gets the distinct impression that he's trying too hard to make this book accessible.
But even despite these flaws, this is an excellent introduction to chaos theory, and worth reading for scientists and laymen alike. This book makes you want to learn more about chaos theory, and does a good job at making chaos accessible. It was written over fifteen years ago, though, so a more recent book on chaos would be a good supplement.