Continuity mistake: In book I when Michael leaves to see his father at the hospital, the narrative text states that Kay Adams would not see him again until three years had passed. When they are reunited in book VII it is often stated that they've been apart for two years, not three.
Continuity mistake: The war between the families is referred to as the Five Families War of 1946 at the end of book I. Later on it's suddenly the Five Families War of 1947, even though it begun with Michael killing Sollozzo and McCluskey in early 1946.