Corrected entry: In the opening scene, the officer of the watch and Aubrey couldn't even spot the French ship with the telescope through the thick fog. But then, how was the French ship able to fire at Surprise with such accuracy? Their line of sight would be just as bad as the British.
Correction: The French ship is a 44, whereas SURPRISE is a 28. It is possible that her masts are higher, allowing lookouts in the tops to see the topmasts of the aproaching British frigate. Depends on how deep the fog bank is, but I've seen similar things at sea on more modern ships.
Factual error: When performing the burials at sea after the final fight with the Acheron, the body on the plank is covered with the wrong ensign. The one shown is not the Union Jack created after the 1800 Act of Union. The correct ensign would be the flag of Great Britain, which does not have the saltire of St. Patrick (the diagonal red "X").
Suggested correction: The story takes place in 1805; the Union Jack is therefore absolutely correct.
Correction: It would also be possible that the Acheron could locate the surprise by sound. They had just beat to quarters, which made a lot of noise; now the ship was resuming normal operations, with the bell being struck and people chattering and working normally. Noises carry extremely far and loud over water.