Lots of issues. The idea that Kay had an affair while Mike ws in Sicily is ludicrous. Kay was pining for Mike the whole time as evidenced by the fact that she came to New York unannounced and tried to get Tom Hagen to accept a letter for Mike.

Also, this book posits that Mike was already into running drugs while he was still learning the family business from his father. Mike would never have gone behind the Don's back and done such a thing.