Special mention to the earlier reveal that the Enterprise herself is hiding on the ocean floor.
The Enterprise leaving the ocean is awe-inspiring in a subtle way, one often overlooked in ST: they're only using simple thrusters to power themselves out. While full specs of starships are uncommon, it's certainly a fact that they weigh at least several hundred-thousands of tons, if not more on the largest. In space this isn't too much of an issue once they pick up momentum, but the Enterprise is under the gravity of a planet, and dealing with the crushing pressures of an ocean. Yet their thrusters are fully sufficient to have them rise out of the ocean, looking all the world like a god to the Nibirans, and for good reason at the power needed to lift a starship under said conditions.
Fourwords from John Harrison: My name is Khan. Cue audiences freaking out.
Later, him just shrugging off Kirk's attempts to beat him up.
Kirk himself does well against the Klingons. He goes toe-to-toe with a bunch of them in hand to hand combat and survives, despite being physically weaker.
Spock and Uhura also get to do some damage too. The former shows to be a damn good shoot while the latter knifes a Klingon in the groin.
Uhura walks right up to a squad of Klingons, looks their leader right in the eye and appeals to the Klingon code of honor to ask for help finding Harrison. It doesn't work, but she gets a hell of a lot of points for trying.
Kirk: [as he and Spock watch Uhura approach the Klingons] Whatever it is, it isn't going to work. Spock: It is the only logical solution. If you interrupt her now, you will not only incur the wrath of the Klingons, but that of Lieutenant Uhura as well.
To clarify: Spock does give Khan back the torpedoes, but without the cryotubes that Khan really wants. He had McCoy successfully remove all the cryotubes from the torpedos and keep them in the medbay. Spock then beams them over to the Vengeance and sets off the automatic timer. You can bet that he's "laughing at the 'superior' intellect."
Spock vs. Khan.
Spock hauls ass after Khan in a marathon sprint, easily overcoming every obstacle in his path - which includes a four-meter vertical leap and a thirty meter diagonal drop. Between speeding aircraft. The staccato beat of Spock's footfalls state his intentions quite clearly - "Khan, your scalp is mine, you're just too stubborn to save yourself the asskicking you have to know that I am about to give you by tearing it off yourself and handing it to me in advance."
Even better, Spock wins the first phase of the fight by attacking Khan where he's most vulnerable: his mind.
Also Khan shrugging off the Vulcan nerve pinch, painfully, but still successfully. Normal people just collapse into a boneless heap.
Khan has spent half his time kicking the ever-loving hell out of every human he meets... and then he goes up against an extremely pissed-off Spock, and discovers Vulcans are a lot tougher than normal human beings.
Kirk punched Khan repeatedly with literally no result, yet Spock breaks his arm, flips him a couple of times, punches the tar out of him, and even assaults Khan's mind. Hell, if Uhura hadn't intervened, Spock would have successfully killed him. Beware the Quiet Ones indeed.
Hell, she managed to save both men from being beaten to death at each other's hands. Saving Khan as mentioned above, and saving Spock moments earlier, by distracting Khan by shooting several phaser blasts at him, all of which pretty much rolled off him like water balloons.
Spock's Improvised Weapon in the fight, where he just tears a hunk of metal off of the vehicle they're on and knocks seven bells out of Khan with it.
Spock breaking Khan's arm is also a nice little Call Back to an earlier taunt from Khan to Spock: "You cannot even break your orders, Mr. Spock. How can you expect to break bone?"
Spock has extra credit for winning that fight, considering that going by the old Star Trek canon, an enhanced human like Khan is five times stronger than a normal human, whereas a Vulcanian is only three times stronger.
Khan crushing Admiral Marcus' head.
John Harrison/ Khan: YOU SHOULD HAVE LET ME SLEEP.
The entire Enemy Mine between Khan and Kirk is awesome in itself, particularly when they're shooting across space to enter Admiral Marcus' ship.
The Enterprise has been badly pummeled; its warp drive is down, the auxiliary power is failing, it's got multiple hull breaches, and it's losing orbit and about to crash into a planet. It dips below the clouds... and then rises back above the clouds, its restored thrusters blasting at full power. It'll take more than gravity to take down the Enterprise!
This incidentally happened because, with his ship falling out of the sky, Captain Kirk made the ultimate sacrifice, giving his life where in another universe, Spock did the same.
Even if it exactly mirrored Spock's death from Wrath of Khan and even if it was only temporary, Kirk finally got a death worthy of him!
Scotty saving the Enterprise by forcing the Vengeance to reboot, taking most of its systems offline in the process. Man's a miracle worker.
Scotty refusing to bring the suspect torpedoes aboard ship. Bringing them aboard when he doesn't know what they are or what harm they might do would be complete dereliction of his duty as chief engineer; so he refuses to do it, and when he can't reason with Kirk, he resigns on the spot. Everyone is uneasy about the mission, but he's the only one who forces the issue, even though it costs him his ship and his career. For a character who is usually comic relief, it's an impressive principled stand against Just Following Orders.
Kirk makes an offhand Badass Boast while escaping with Spock and Uhura from a pursuing ship.
Spock: This ship has no offensive capabilities. Kirk: It's got us; give me all six fuel cells.
Carol attempts to try to dissuade her father from killing everyone aboard the Enterprise. She fails as he beams her off the ship, but she did give it her all and slaps her father. She also manages to elbow one of her dad's mooks in the face.
Carol: I am ashamed to be your daughter.
Acting Captain Hikaru Sulu, who is forced to take command with Kirk, Spock and Scotty off the ship. He's never sat in the big chair, and Bones is convinced that he can't bluff Harrison into surrendering. John Cho then channels George Takei's Captain Sulu and throws down the gauntlet, telling Harrison on an open channel exactly what he will do.
Sulu: Attention: John Harrison. This is Captain Hikaru Sulu of the USS Enterprise. A shuttle of highly trained officers is on its way to your location. If you do not surrender to them immediately, I will unleash the entire payload of advanced long-range torpedoes currently locked on to your location. You have two minutes to confirm your compliance. Refusal to do so will result in your obliteration. If you test me... you will fail.
Kirk taking Harrison's ship down after he attacks Starfleet by tossing his weapon into the ship's turbine.
As the Enterprise is falling and the gravity is off, Kirk and Scotty have to make their way to Engineering to reboot the ship. A falling piece of metal throws them off their path and as Scotty and Kirk barely hang on to the rail, Kirk's grip slips and Chekov appears just in time to pull them up from certain death.
Villainous example. The first time the USS Vengeance shows up and how she proceeds to chase the Enterprise down in warp and deliver an utter No-Holds-Barred Beatdown.
Spock saying William Shatner's famous line from Star Trek II. You know which one.
Kirk: Let me explain what's happening here: You are a criminal. I watched you murder innocent men and women. I was authorized to end you! And the only reason why you are still alive is because I am allowing it. So Shut.Your.Mouth.
We hear the origin of the show's famous Opening Narration. It turns out to be something Captain Pike said to Kirk.
When the Vengance has the Enterprise at gunpoint, Kirk attempts to bargain with Marcus, stating that the actions of his crew were at his orders, and offers to surrender on the condition that his crew be spared. It's at that exact second that Kirk fully knows the responsibility of sitting in the captain's chair.
He still manages to sacrifice himself for the still-living crew, by climbing into the radioactive chamber. The awesome comes in when Scotty said that they wouldn't even be able to make the climb before the radiation killed them, but not only did Kirk make the climb, he still had the ability to keep going until the damn reactor was fixed. And still have enough gas in his proverbial engine to crawl all the way back to the door.
And after all that he still manages to cling to life long enough to be put into stasis.
Spock managing to convey "You're a dead man, Khan!" after Kirk is killed without EVER speaking a word until afterwards.
Pike telling Kirk exactly what he's needed to be told since he drove that damn car off a cliff. He is arrogant, he doesn't know how to follow the rules, he does think the rules don't apply to him, and he is a pain in the ass. Kirk desperately needed some tough love punctuated with a verbal asskicking, and Pike was more than happy to supply both. Even better, when push came to shove, Kirk shut up, listened, and learned the lessons he needed to learn. A CMOA for Parental Substitutes if anything ever was.
For some reason, the scene with Spock Prime stands out as awesome. "I'm not allowed to interfere by giving you knowledge of the future. It could corrupt the timeline." And then as they look like they're getting bummed out about that, Spock Prime then goes "That being said..." and goes on to tell them all about Khan. And it really says something that Spock considers Khan the most dangerous thing that the original NCC-1701 ever faced, considering all the mad gods, the planet-destroyers, mutants, entire empires, and worse that they faced. And all of this is with the knowledge that for Spock, it's been something like one hundred and fifty years since he faced Khan, and in another dimension, and still it left a psychological scar on him, one that says "Khan is involved. THINGS ARE DEADLY. SERIOUS."
It's very subtle, but Spock's delivery when he says, "Vulcans cannot lie. The torpedoes are yours." His expression and tone perfectly match those he gave the Vulcan High Council in the first movie: it's basically a big old Vulcan "fuck you."
Kirk confronting Admiral Marcus on the Vengeance. Admiral Marcus is the head of Starfleet - he's not just Kirk's boss, he's Kirk's bosses' bosses' boss. He gives a long speech about how war is coming, and tells Kirk that Kirk will have to kill him before he surrenders. Kirk's response: "I'm not gonna kill you, sir. But I could stun you and drag your ass out of that chair."