Factual error: When the royalist troops land in France, Hornblower's division has the job of transporting 2 12-pound-er naval cannon. These each weigh in excess of 18cwt, and yet 3 men unload them from the ship's boat. In actuality, the gun barrels were transported suspended in the water between two boats, then dragged up onto the beach.
Plot hole: When it becomes apparent that the British will have to retreat, Matthews is instructed to disable the cannon. He reports to the Mr. Kennedy that he has spiked the cannon (a method of temporarily rendering the gun useless) and that he had, "blown the trunnions off for good measure." This would have turned the cannon into rather large boat anchors, so why bother investing valuable time in spiking them?
Plot hole: Following Pellew's meeting with Lord Hood, he tells Hornblower that they had to get back to Plymouth as quickly as possible. The next scene depicts them at fleet landing in the Pool of London, with a number of battleships at anchor. Line-of-battle ships simply were unable come that far up the Thames. Should it have been intended to depict that they had, following a two-day trip via carriage to Plymouth, gone aboard the Indefatigable there, it is illogical for the French troops to march all the way to Plymouth. A quick glance at a map of Britain supports this contention.