A Father's Great Expectations - S1-E1
Factual error: When JFK leaves to become a PT-boat commander he is wearing full lieutenant's rank insignia. He was actually a lieutenant junior grade when he took command of PT-109.
Factual error: Admiral Burkley, Kennedy's physician, is depicted wearing the insignia of a full admiral (one wide and three narrow rings) and the star of a line officer above his cuff rings. In actual fact, Burkley was a rear admiral (one wide and one narrow ring) and medical officers wear an oak leaf above their rank rings.
A Father's Great Expectations - S1-E1
Factual error: The officer who phones Joseph Kennedy Sr to tell him that JFK is missing in action introduces himself as a commander at the War Department. However, he is wearing naval captain's rank insignia and (since the War Department only dealt with the army and JFK was a naval officer) would actually work for the Navy Department.