I just read the Preface and am currently reading the Prologue of this book and it struck me that the writing style was more like popular rather than academic history books. The author seems to be a respected academic, and the book is from Princeton University Press.
So my questions are:
Are the facts and theories presented in this book correct and thorough?
Are there any other academic books about this period or subject?
He did an AMA a year ago if you're curious.
Yes insofar as theories about what happened 3000 years ago can be 'correct'. At some level it's still quite vague - the collapse happens due to a number of reasons- but that is significant in that earlier studies tended to singular causes for the collapse.
Joseph Tainter has a general book on the collapse of societies, Richard Drews has a couple around the LBA and collapse, and at the risk of suggesting Wikepedia's list of books, it's actually a reasonable list of papers and books on the matter, but you might want to wait for someone with a speciality in Mycenaean/Aegean matters, as I can only cover the Levant.