Just reading the reviews from my perspective as a student of Jewish history and religion, I find much to object to, although I don't necessarily disagree with his ultimate conclusion that the Jewish people believed so much that they were a special people, protected by God, that they evolved into one and survived in Houdini-like fashion. From one example in Hertzberg's review, regarding that there is "no evidence" that Jesus was a student of Hillel, struck me as a very uninformed answer. First, the two were 100 years apart. Second, Johnson seems unaware that there was a School of Hillel (Beis Hillel) that continued his teachings and philosophies in the years contemporary with Jesus -- therefore Jesus could have studied (and probably did study) with Beis Hillel. Another criticism is his failure to take notice of the Sephardic Jewish world in Moslem-occupied African and Asian lands, including the Lavant. If true, then that misses a great deal of history including Maimonedes and his great contributions to Jewish thought and philosophy, Nachmanides, and the codification of Jewish Law by Rabbi Joseph Karo. It is unlikely any Jewish history would miss either or the amazing scholarship of Sephardic Jews in the Iberian Peninsula prior to the 1492 expulsion.
The reviews also take him to task for relying on secondary sources. I don't consider that a serious problem as he would need mastery of Hebrew, Aramaic, Arabic and Yiddish. Furthermore, to get a real grasp of rabbinic learning and philosophy from primary sources, I believe would take years of study of hundreds of volumes of books -- something most historians choose to forego (and why many historians do poorly when trying to describe Jewish history regarding religious teachings).
But all in all, I respect the historians who reviewed his books and their mostly positive conclusions.