Plot hole: When Hornblower arrives home from the Pacific, he meets his son, a baby in a cradle. He is given the Sutherland, sails to Spain, is captured and escapes, and returns to England a hero..all in under a year. However, upon arriving in Portsmouth to see the Admiral, he visits his son, now a child of 3 or 4.
Plot hole: During the second engagement with the Natividad, Hornblower is advised that the surgeon is dead. The duty station of a surgeon in battle is in the cockpit on the orlop deck, far below the waterline. The odds of a cannonball penetrating there would be longer than its penetrating the cable tier.