Young Lord Blakeney is terrified by his first taste of incoming grapeshot, but Jack reprimands him gently: "We stand tall on the quarterdeck, son. All of us."
Our heroes' vessel is crippled and the day seems to be lost before it's even truly begun.
1st Lt. Pullings: Your orders, sir? Capt. Aubrey: Call the gun crews to deck. Rig man-ropes over the stern and pull the boats in. Put us in that fog, Tom. [Pullings' worried expression melts away into one of unrivaled admiration as he looks out at the pursuing Acheron, then back at Jack]
Doctor Stephen Maturin performs an advanced trepanning operation on 'Old Joe' Plaice after the Acheron's first attack leaves him with a shrapnel wound that has fractured his skull and a 99 percent chance of slow, lingering death. Not only does the doc ensure he doesn't die, but the grizzled sailor eventually regains his voice and returns to full fitness! A "physician he is" indeed.
Just for a taste of how awesome this is, even in modern times with advanced hospitals, depressed skull fractures have a low survival probability.
"This is the second time he's done this to me. There will not be a third."
The author of the books the movie is based on often opened with apologies. Typically, he apologized for anachronisms (including eau de Cologne in a scene 10 years before it is recorded as appearing in England, or putting a naval battle before the grape harvest when it was known to have occurred after the grape harvest...), but on a few occasions he apologized for toning things down. In his own words, "When one is writing about the Royal Navy of the eighteenth and early nineteenth centuries it is difficult to avoid understatement; it is difficult to do full justice to one's subject; for so very often the improbable reality outruns fiction. Even an uncommonly warm and industrious imagination could scarcely produce the frail shape of Commodore Nelson leaping from his battered seventy-four gun Captain through the quarter-gallery window of the eighty-gun San Nicolas, taking her and hurrying on across her deck to board the towering San Josef of a hundred and twelve guns, so that 'on the deck of a Spanish first-rate, extravagant as the story may seem, did I receive the swords of the vanquished Spaniards; which, as I received, I gave to William Fearney, one of my bargemen, who put them, with the greatest sang-froid under his arm.'"
Captain Aubrey's toast, "Here's to wives and sweethearts—may they never meet!", especially for those familiar with the books.
This was an actual toast said in the officers' mess on Saturdays. Typically, one officer would say the first part and the second would be said by the youngest present.
Maturin gets an unmitigated awesome moment to himself for the last third of the film, when he operates on himself to remove a bullet. Compounded by his pausing to ask Jack Aubrey (who is certainly no shrinking violet) if he, Jack, is all right.
"LET FLY!" The Surprise can achieve some awesome speed.
Lucky Jack's Rousing Speech to the whole crew, before their assault on the Acheron.
Aubrey: Right, lads. Now I know there's not a faint heart among you, and I know you're as anxious as I am to get into close action. But we must bring him right up beside us before we spring this trap. That will test our nerve. And discipline will count just as much as courage. The Acheron is a tough nut to crack. More than twice our guns, more than twice our numbers. And they will sell their lives dearly. Topmen, your handling the sheets to be lubberly and un-navylike, until the signal calls for you to spill the wind from our sails. This will bring us almost to a complete stop. Gun crews, you must run out and tie down in double-quick time. With the rear wheels removed we've gained elevation, but without recoil, there will be no-chance to reload, so, gun captains, that gives you one shot from the larboard battery. One shot only. You'll fire for her mainmast. Much will depend on your accuracy. However. Even crippled, she will still be dangerous. Like a wounded beast. Captain Howard and the marines will sweep their weather deck with swivel gun and musket fire from the tops. They'll try to even the odds for us before we board. [nods at Howard, who smiles warmly] ... They mean to take us as a prize. [the crew chuckles at this] And we are worth more to them undamaged; their greed... will be their downfall. [pauses] England is under threat of invasion. And though we be on the far side of the world, this ship is our home. This ship, is England. So it's every hand to his rope or gun. Quick's the word and sharp's the action. After all, Surprise is on our side. [crew laughs uproariously and huzzahs]
When the HMS Surprise drops her disguise as a whaler. The ship halts, the true colors are run up, the marines come out from hiding under canvas, and the cannons come out to blast the Acheron's mast to splinters. After the main mast topples, the Surprise sweeps in behind and blasts the Acheron from behind with her other battery.
Also, the one-armed 12 year old Midshipman Blakeney countering an attempted hull breach with one of his own and subsequently leading the second ship boarding party.
Blakeney: Arm yourselves! We must board them! Follow me! [fires flintlock pistol into a French sailor's face at point-blank range]
Jack beasting his way through the mid-decks with sabre, pistol, grenades and anything else at hand; he's such a whirling dervish of destruction that eventually the French sailors would rather flee and surrender rather than fight the Captain of the HMS Surprise.