The paradox about this third volume in the series is that although there's a lot of action, and many things happen, nothing happens in terms of character development or new ideas about communications between the worlds.
First off, this volume is not readable as a stand-alone. If you are new to the series, book 3 would make no sense whatsoever unless you read books one and two first - so if you're going to order this one, order all three. Second, although we have no new ideas and very little in the way of character in book 3, if you're reading the series, you'll have to read this one, or else book 4, when it comes out, will be unintelligible. In my opinion, book 3 should not have been published as a stand-alone at all, with its beginning in the middle of a conversation between two characters and its end in a cliff-hanger; Stross should have saved it and combined it with whatever will be in volume 4, for a larger book, one with more of a satisfying plot.
Such as it is, the plot of this book consists entirely of getting a few more of our-world characters aware of the existence of the Clan's world, and killing off a few important characters in each world in order to make way for whatever happens next. We get only about 5 seconds' worth of Miriam working on her technology-transfer business, and about 3 seconds of her flirting with James Lee, of the family that discovered the New Britain world, for romance. The rest is spies spying and the military plotting to blow things up (several different military organizations, in more than one world-line) and occasionally doing so.
As alternate history goes, since Miriam spends almost no time in New Britain in this volume, and most of her time in the Clan world is spent on internal business of royalty and etiquette, we don't really find out anything new about the differences between the worlds.
In short, unless you're interested in a few drug busts and a bit of military paranoia, the only thing to recommend this book is that it's a necessary bridge in the series. You could wait to cross that bridge until book 4 comes out, so that you actually have a destination, and then buy both volumes together.