[Disclosure: review based on a previous edition of the book (2004), before the new "Complete" series came out. The publisher doesn't allow us to look inside, so I cannot check whether it is the same. My edition does not have an index, for example, but I am supposing they have had the sense to change this. The earlier edition is still available from Amazon, but without CDs, so I am reviewing here, since this is the version with CDs, which I have.]
Firstly, I confess I've had this book a while, and referred to it many times, but never gone very far with it. Still, I blame that mainly on the book. Now that I have Lambton and Thackston, I'm getting more motivated again, and a decade ago, I used Mace's earlier Teach Yourself with some success and much interest.
This book doesn't really impress me, I think because it just seems too light. Each chapter begins with a simple dialogue, from which grammatical points and vocab are drawn out, but the vocab is not very interesting, and the grammar is quite basic. Dialogues are trivial, and knowledge builds very slowly. I think that is fine for some learners, but then an unreasonable amount of time is spent on some orthographic conventions that do not affect pronunciation - such as the exact use of the ezafe. A waste of time, I feel, at the early stages, and it could have been confined to an appendix.
I have only recently figured out what is really wrong with this book, which is why I'm writing this review now. It doesn't mention the definite direct object marker until chapter 14 (of 21). If you're wondering how it survives until then without one of the most common grammatical features of Persian, it's simple: you spend the first six chapters with only one verb, namely, "be". I've checked fairly carefully, and I'm pretty sure there isn't any other verb there. That means you get riveting dialogues like, "Are you a student." "No, I am not a student, I am a photographer." "Are you at home?" and so on. Then you graduate to another verb, "have," but it still avoids a single definite, direct object, by quantifying everything, as in, "I have one cat." If it was "*a* cat" you'd need the indefinite marker, but even that has to wait until chapter 8. If you can imagine a conversation with two verbs, this might be for you. By the end of the book, it has covered the future tense and the subjunctive, which is pretty good, but even relative clauses, a basic construction in any language, are confined to an appendix.
Grammatical descriptions when they are given are good, although a little long-winded. There are also possibly too few examples to go with the too-long descriptions. The CDs are excellent, or at least surpass the book in many ways. I would say it may be value for money just for these, but they are mainly designed to accompany the text, so your main motive here is the lack of alternatives - the good books (such as Thackston and Lambton) do not have CDs (I think there is an expensive casette for Thackston, which is a little primitive).
In short, if you are a self-learner, this might be quite ok if you need a really basic introduction, and if you hate lots of grammar. Expect to learn slowly, but that is better than not at all.
Answer key: yes.
Vocab both ways: Yes. ~1000 words each way in back of book.
Exercises: to and from Persian. Mostly very basic.
Transliterations: Up to chapter 10, thereafter, vowel markers for all vocabulary, including back of book. Some vowel markings for dialogues.
Readings: Only very simple, mostly conversational, one substantial one at the end of the book.
Extra features: good table of present stems of irregular verbs.