When escaping from the battery, Styles needs to walk ankle deep through waste when moving through the latrine, same as the other men. When fighting in the beach, at the very next scene, their trousers, stockings and shoes are all spotless.
Almost certainly the result of deliberate chuckles by the film makers, two filler scenes showing ships under way with crew members scurrying around have voice-overs calling orders that make no sense. The first is "Splice the mizzen!", which can't happen because the mizzen is the third (back) mast on the sloop being shown and a splice is a means of joining or adding a loop to a rope (not that many pieces of rope are called 'ropes' on a sailing ship!). The second is "Weigh the sails!", which is equally goofy because sails can be 'handed', 'reefed', 'sheeted', 'brailed' and lots of other things, but only anchors are 'weighed' when they're taken up as in "anchor's a-weigh, Sir!", and even that the ship is now 'under weigh'.
When Hornblower's Hotspur and the French frigate Loire cross paths passing honors, the Loire's bow wave and wake look distinctly artificial since they do not effect the water around the ship, revealing miniature work and a CGI effect added in post-production.
In the end, when Captain Hammond shoots himself, there is a large blood spray which is obviously a CGI effect edited in post-production, as it disappears too fast and there is no sign of blood on the floor or on Hammond's head later, when he is lying on the floor.
At the engagement with the Loire, Major Côtard is hit across the cheek by a musket shot. However, his scar disappears and reappears during the rest of the film.
In the opening scene entitled "Portsmouth 1803" when the camera pans from right to left, a rowboat can be seen rowing in the same direction, but when the camera pauses, the boat, actually a CGI effect, does not catch up to it and seemingly disappears.
When finally revealed as the traitor, Wolff is seen eating lobster and scallops, boasting about the skills of his chef. However, while expensive and luxurious food items now, in the 1800's lobster and scallops (along with most shellfish) were considered peasant food, and in Britain was often reserved to feed prisoners and pigs. In reality, an officer like Hornblower would sneer at Wolff for eating such items.
When discussing the threat of a French invasion on board the flagship, captain Hammonds makes a mocking remark about Napoleon issuing orders from Windsor Castle instead of Versailles. However, Napoleon never lived in Versailles: the imperial residence was Tuileries Palace, in Paris. By the time the action is set, the Palace of Versailles had been abandoned for over a decade, having been looted by the French revolutionaries, and would not be restored until 1870, and never used again as official residence.
A Radar reflector can be seen tied in the halyard above the national colors of the Hotspur.
When Hornblower and the landing party are captured, they are incarcerated in a small room and seated on the floor with everyone's ankles secured and chained into wooden stocks. They affect their escape by using the many ropes and block and tackles that are in the room and install an intricate pulley system using hooks attached to the beams and ceiling fixtures, unless one of the landing party had the arms of an orangutan, they would not have been able to set this up.
Admiral Pellew reminds Hornblower that; "In time of war a captain may not sleep out of his ship". The statement is only partially correct. This rule applied only to the Channel Fleet (of which Pellew is the commander in the story).
In Hornblower: Mutiny (2001), Matthews is shown to be Boatswain of the HMS Renown, a 74 gun ship of the line. As such, Matthews would have been a Standing Officer, rated his own cabin, and considered to hold a Navy Warrant, setting him apart from ordinary seaman. With such experience, it makes absolutely no sense that he would now be seen showing up to serve on Hornblower's ship, who was a non-rated Commander, and joining the ship by signing the books as a seaman. This would have been considered a major demotion when Matthews could easily have remained a Boatswain on a larger ship.