Politkovskaya's book is important in the sense as it gives a voice to people that is not heard in other books about contemporary Russia. Especially the chapter "Tanya, Misha, Lena and Rinat - Where are they now?" where she looks up people that she used to know in the 70s, gives a remarkable description of personalities that anyone that gets to know Russian's personally will be able to recognize.
A weakness of this approach is that it is difficult to recognize and appreciate these personality-types without personally knowing enough Russians to see what she is talking about. Unless you know Russians personally it will also be difficult to experience and take in, how many simply will refuse to read, know and take in her story either because it is something they have decided to act as if these things never happened - focusing on this is negative, or simply because they are very emotionally difficult to discuss. This attitude and feelings among ordinary Russians is in my view far more important than the authorities attitudes towards her writing.
I agree with the other reviews that claim her writing is very emotional. This is a problem because it makes me suspicious of her writing, even when what she tells is probably completely true. By being less emotional she would without doubt come through as more trustworthy, that is especially important because we to a large degree only have her side of the story to hold on to. Though considerably more moderate than Litvinenko and Felshtinsky's "Blowing up Russia", I find myself having some of the same mixed emotions about some of the consparicy-like claims that come up in the book, where we only have whether we believe the author or not to hold on to. Though experience have learned me that few seemingly over-the-top fantastic rumors can be ruled out when it comes to Russian politics, I am still laved with mixed emotions.
Her personal approach also leave the basic, structural facts that is important to understand contemporary Russia in the background. Gaidar has used the relevant comparison of Russia in the 90s with the last similar desperate economic situation in Germany in the 30s. About 15 years after the democracy was established in Germany, Hitler came to power under similar economic conditions. Who ever Putin is, he is like a boy-scout in that perspective. Politkovaskaya fails to give the political and economical understanding to put things into perspective. As another review states, you will not find what progresses Russia has made under Putin in this book. It is not that critical though, as long one can get that perspective from other books. Polikovskaya gives an understanding of the people acting under this cicumstances that I have seen no other books on contemporary Russia.
Politkovskaya has written other books and articles on Chechnya, I think Chechnya has got too much coverage in the book, compared to other topics. It might be that she should have chosen a different title, instead of writing relatively less about Chechnya though. It is nothing wrong with writing many books about Chechnya, it is just that the topic "Putin's Russia" is considerably broader than that.
Another review claims you can not find Politkovskayas books in Russia. I can confirm that I have found them in English in ordinary book-stores and Russian friends confirms they have fond them too.
Do read this book. Make sure you fill out the picture with other books on the Putin era and the political and economical development in Post-USSR Russia though.