Hornblower is released from his solitary confinement in the underground cage, where he has been (presumably) for several days, yet he is clean shaven when returned to his shipmates.
During the dinner scene, Sir Hew Dalrymple toasts the King and all the diners rise to reciprocate. It has been long standing etiquette that the monarch is always toasted whilst seated, something the attendees would have known given their social standing.
In the opening shot, when a rowing boat comes close to the shore, a helicopter can be heard.