I am writing this review from the perspective of a physicist (w/ Ph.D.) looking to start a career in finance. Currently, I have spent about a month studying the book, and can say that I have a good grasp of the first half.
Overall, I feel that this is a very good introduction to the field of mathematical finance. The canonical suggestion for people of my background is to start with Hull's book (Options, Futures & Other Derivatives with Derivagem CD Value Package (includes Student Solutions Manual for Options, Futuresd Other Derivatives) (7th Edition)). I disagree---not only is that book too expensive, if you have an advanced degree I feel that you should start with a more advanced textbook. I feel that this book is written at an advanced undergrad/intro grad level text, and should keep the reader interested. Moreover, Joshi does a very good job of explaining things from many different angles, which is very helpful if you're just learning the field. The problems tend to be easy, and you can work through this book in two or three months without much effort, except in Chapters 6 and 8 (see below).
There are a dozen or so longer computer projects in the back, and Joshi recommends his readers complete all of the projects before starting to look for a quant job. I think this is probably a good idea, and one should supplement their C++ coding with Joshi's other book (C++ Design Patterns and Derivatives Pricing (Mathematics, Finance and Risk)). Before attempting either the projects or Mark's other book, you should be familiar with classes and inheritance and all the associated goodies (virtual functions, etc.). This will allow you to get the most out of both of Joshi's books.
Another wonderful resource associated with this book is Mark's discussion forum (see the Preface), where he answers questions personally (or, perhaps, has a graduate student to do his dirty work). Either way, this is an invaluable tool for self study, as Joshi (or his ward) answer questions there regularly, and I've never had to wait more than a day or two for a response.
That being said, I do find the writing style to be too prosaic at times. For me, I feel that the author belabors some points while leaving others unaddressed. Other notational/stylistic issues really bugged me---for example, the author has a habit of writing expressions instead of equations (i.e. writing just the right hand side of an equation). This drove me nuts, as it diminishes the value of the text as a reference because you can't scan through to find an equation. (If you think I'm crazy for mentioning this, I warned you!) I also felt that Chapters 6 and 8 took a lot of work and seemed needlessly complicated, though this may represent my own shortcomings as opposed to the author's. I felt as if I was thrown into the pool, so to speak, in Chapter 6, which didn't provide enough background for understanding what is going on in Chapter 8. Readers who have a solid background in real analysis and probability theory will probably fare better. Chapter 6 is rife with typos, so careful reader should keep the errata from Joshi's website close at hand.
In summary, this book is a cross between a formal mathematical introduction to the subject, and a primer on practical application, tending more towards the former than the latter. It distinguishes itself from other purely mathematical introductions in its style: instead of the ``theorem-proof-corollary-proof-useless example'' format of a math book, Joshi thoughtfully examines the important concepts from complementary angles. And while I feel that it is a very good introduction to the field, you simply cannot learn all there is to learn about the field from one introductory textbook, so I suggest that interested readers supplement their study with a more qualitative/less math-y reference (I'm reading Tim Crack's Basic Black-Scholes: Option Pricing and Trading) and a textbook which focuses more on the mathematical tools (I particularly like Baxter and Rennie's Financial Calculus : An Introduction to Derivative Pricing). By combining this textbook with a few other references, and taking Joshi's Table of Contents as the syllabus, I feel that the interested reader should be able to develop a very full understanding of the rudiments of this interesting field.