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.
Continuity mistake: When the Spanish demand Hornblower surrender his ship, the battleship fires two shots.the first shatters the topsail spar at the jeers, bringing it down, and the second.shatters the once again undamaged topsail spar outboard of the jeers, bringing it down again.
Plot hole: As the Spanish fleet looms out of the fog, Hornblower is able to identify individual ships, a remarkable feat since every ship is wearing the same paint job.