I write only to second the first two reviews and bring the debate up to date. When 'Testimony' first appeared in 1979, the naive political attack of the then Soviet union obscured the more profound criticism of those who knew Shostakovich well - namely, their incredulity that a personality as complex and secretive as Shostakovich was would ever have revealed himself to such a degree to a comparative stranger. Volkov did not help his cause by refusing to disclose the bulk of the transcript for many years.
But when he finally he did so, it turned out that his practical reasons for keeping the ms. to himself were correct - for inspection revealed such obvious indications that Shostakovich had by no means endorsed the book as to end the controversy and Volkov's reputation with it. This analysis is detailed in the Shostakovich Casebook, and also in the Bard Festival handbook. The material is not at all dry, but quite interesting to people wondering how working historials and biographers actually do business.
It is worth noting, however, that even the harshest critics acknowledge the enormous service 'Testimony' performed to Shostakovich, in presenting the West with a different image of the man than simply genius-cum-party-hack. It caused many people (myself, for example) to take a look at a musical accomplishment that was prodigious by any standard. The revitalized interest in DDS's chamber music, songs, and what were once considered his minor works, has led to a massive and long overdue appreciation of a towering musical genius. Volkov is owed a debt of gratitude for that that no one denies.