Factual error: Reference is made to the king as George II, and Captain Sawyer as one of "Nelson's own." However, Nelson was only about two years old when King George II died. The Napoleonic Wars were during the reign of King George III.
Factual error: Hornblower's plan is to sail Le Reve south from Gibraltar to give him ample sea room before he heads for England. Generally, the prevailing wind through the Straits is westerly, unless there is a Levanter, yet Le Reve is shown on a port tack when it should be on a broad reach. The fog that comes up would not exist in a gale-force Levanter.