I finished it recently and couldn't help but feel like that the book paints a rather negative image of many of the main characters that were involved in the dealings of the succession. Be it his wife Aisha that comes off as extremely power hungry, Ali, ultimately, as pretty naive and proud in his dealings with Muawiya, the governor of Syria.
It was a very interesting read, but I caught myself thinking more than once: "Are you serious? THAT happened? By the people closest to a man supposedly free of fault?"
I am not anti islamic at all, and don't seek to reinforce any prejudice, quite the contrary. The years following Mohamed's death seem incredibly brutal though on many levels and I would love to hear an expert's opinion on it. Thank you!
I hope my answer isn't too late! I haven't read this book, but from my experience with her other book on Muhammad, you should take all her assertions with a grain of salt. She is not an expert on this field and her approach to sources is very old-fashioned - she might be repeating what the sources said, but sources on early Islam are deeply flawed and from a cursory glance through Amazon reviews (I know...), she apparently only used sources from the Shia perspective, which naturally painted Ali as the 'good guy' and Mu'awiya as a schemer, when the latter was an extraordinarily able leader. For a brief look at the problems involved, check out this thread, though the fact that the top answer has to be clarified by other answers demonstrates just how complicated this period is even for modern historians - there is no 'definitive' view of what actually happened, only many many theories. You should also check out the FAQ for a few other answers that covered the methodological problems we face in this field.
I would recommend Hugh Kennedy's The Great Arab Conquests: How the Spread of Islam Changed the World We Live In for a more reliable perspective, as Kennedy is a leading scholar on early Islam and his book covers the power struggles of the Caliphate much more accurately than Hazelton (that is, he used many sources and acknowledged the problems of working with these sources), but is still a book for the general reader :)