Hornblower's frequent, vivid imaginings of what could happen to him in battle—shattered limbs, getting cut in half, the agonies of surgery, infection and gangrene and a painful drawn-out death.
The situation with Captain Sawyer in Lieutenant. The captain of a ship on detached service was essentially the emperor to those aboard. With no higher authority nearby, he could act how he saw fit, no matter how brutal or tyrannical. In this case, the lieutenants can't defend themselves against his paranoid hostility and have to watch as the ship sinks into indiscipline. Mutiny isn't much of an option, because the Admiralty is really biased against mutineers no matter how justified, but if they don't mutiny, Sawyer is going to bring totally false and yet deadly charges against them anyway. There is just about nothing they can do... except, perhaps, engage in some foul play.
In Hotspur, Hornblower returns to his cabin after blowing up a French battery and semaphore (which involved using the body of a redcoat to conceal the fuse) to find that his steward has hanged himself there after pleading with Hornblower not to go out of cowardice and realizing what the consequences of that would be. The description of the body dangling from the ceiling and Hornblower realizing how long it must have taken for Grimes to die are shudder-inducing.
Also from Hotspur, the moment during the retreat from the battery and semaphore where a huge piece of exploded masonry lands on Jones, the captain of marines, and drags his body as it slowly comes to a stop next to Hornblower and Cotard. Both men are, for a moment, mesmerized in horror at the sight.
Jack Simpson. The horrible beatings and psychological torture the audience saw, that would be bad enough. Nothing Is Scarier, though, and the implied stuff he did to other midshipmen must have been awful. Shudder! The way he troubled Clayton and especially poor Archie who was absolutely terrified of him is truly disturbing. Even the tough Horatio contemplated suicide just after several days of Jack Simpson's company. In addition, while they were aboard the Justinian, Simpson was apparently never held responsible for any of his heinous crimes. Captain Keene obviously thought Simpson was an idiot, mocking him with delight during the navigational session, but how come he didn't see how the guys were scared of him? And what about the lieutenants? Adults Are Useless or was Simpson really such a skilled Manipulative Bastard?
The Indefatigable is under attack from several French corvettes, when the recently-captured Papillon comes to her aid. Given that Hornblower has "neglected" to lower the French colors, the corvettes are quite surprised when she abruptly begins firing broadsides into them. One particularly unfortunate ship is blown to splinters when the magazine is ignited. Even Captain Pellieu is horrified by the sight.
Crazy Captain James Sawyer. Captains were absolute masters aboard the ship but when the Captain goes mad, you are doomed. Doomed! Your captain can get you beaten for just a foul look, and sometimes you may experience A Taste of the Lash just for doing your freaking duty. Your life is in the hands of a madman who can dispense a capital punishment and get you hanged right away on the yardarm. In addition, he might happen to be a Death Seeker who doesn't mind taking his whole crew with him. Terrifying.