Before Spock goes down to stop the volcano, his exchange with Uhura is both hilarious and adorkable.
Uhura: Are you sure you don't want me to go instead? Spock: That would be highly illogical as I am already outfitted— Uhura: Spock, I was kidding. Spock: Uh... [looks adorkably confused as Uhura kisses his helmet]
Kirk's Tempting Fate line. Made funnier in that we see the native holding the sacred scroll they were chasing Kirk for, simply drop it after they start worshiping the Enterprise instead.
This becomes a meta joke: awkwardly dressed people wearing weird make-up worshiping the U.S.S. Enterprise... Yep, Kirk violating the prime directive resulted in him creating the Planet of Trekkies.
A deleted scene reveals that during his log, the entire bridge crew all shoot him identical looks of disapproval. Uhura just turns around and walks away as one of the crew members sitting behind Kirk shakes her head.
During the debriefing after the Nibiru mission, we learn what lesson Kirk took from the experience: "Never trust a Vulcan".
Also during the debriefing.
Pike: That's a technicality. Spock: I am Vulcan, sir. We embrace technicalities. Pike: Are you giving me attitude, Spock? Spock: I am expressing multiple attitudes simultaneously. To which are you referring?
That entire scene can pretty much be described as a father scolding his younger son with the older one coming to the younger's aid, with the younger one mad at the older for telling on him.
At one point, Kirk irritably calls Spock "pointy" while ranting at him, causing Spock to ask, "'Pointy'? Is that a derogatory reference—" before Pike cuts him off.
Another conversation between Kirk and Pike at a bar...
Pike:The first time I found you was in a dive like this. Remember that? You got your ass handed to you. Kirk: That is not what happened. Pike: It was an epic beating. Kirk: No it wasn't. Pike: You had napkins hanging outta your nose. Kirk: Yeah, it was a good fight.
And before that, Kirk was making eyes at a pretty girl and was about to make his move when Pike suddenly appears, killing Jim's game.
Kirk is making impossible demands of Scotty: "Give me two seconds, ya mad bastard!"
Kirk wakes up to the Beastie Boys after having a threesome with two cat women.
Just before they head into the meeting with Starfleet's top brass:
Moments before that, upon being told he's answering to a different Captain, Spock gives Kirk the most adorable kicked puppy look a Vulcan can manage. It's funny, heartwarming and Tear Jerker all rolled into one.
Bones insists on a post-mission medical exam on Kirk, including sticking his scanner onto Kirk's cheek. While Kirk is in the middle of a conversation with Spock. On a shuttle.
Kirk: Bones, get that thing off my face.
During the conversation:
Kirk: I'm not taking ethics lessons from a robot. Spock: Reverting to name calling suggests you are defensive and therefore find my opinion valid.
Kirk calls up Scotty while the latter is absolutely wasted at a bar with Keenser.
Kirk: Scotty, it's Kirk. Scotty: Well now! If it isn't Captain James Tiberius Perfecthair! [to Keenser] Heh, did you hear that? I called him "Perfect Hair."
Scotty's declaration: "One day I've been off this ship! One bloody day!"
Scotty huffing and puffing as he runs from one end to the other end of the holding bay of the Vengeance.
Scotty: I'm running... STAND BY. [breathes heavily]
Kirk asks if Spock and Uhura will be okay with working together on the away mission. Uhura, in a tone that makes it very clear that she's still furious with Spock, says they will and walks off. Spock watches her go...
When Kirk asks Uhura to come with them, watch Spock closely; his eyes widen slightly, and you can just tell that he's thinking, "Oh my God, she's coming with us, I'm not gonna cope with this, I'm not gonna cope with this..."
Kirk: Guys. Are...are we really going to do this right now? [Spock and Uhura continue bickering] Uhura: I'm sorry, Captain, just two seconds. Kirk: Uh, okay. Uhura:[to Spock] I'm not the only one who's upset with you. The Captain is too. Kirk: What? Oh, no. Don't drag me into this. [beat] She is right.
Then after narrowly escaping the Klingons through a narrow crack:
Kirk: I told you we'd fit! Spock: I am not sure that qualifies.
When Uhura plays diplomat to the Klingons, Spock has this to say. It's the way he says it which makes you realize that he speaks from experience, and the mental image you get is hilarious:
Spock: "If you interrupt her now you will not only incur the wrath of the Klingons, but that of Lt. Uhura as well."
Made better with how Harrison's expression changes after each punch, going from utterly offended, to confused, to bored and then finally, amused.
Kirk and Uhura in the turbolift and he immediately latches on to Spock and Uhura's problems.
Kirk: Wait, are you guys—are you guys fighting? Uhura: I'd rather not talk about it, sir— Kirk: Oh my God, what is that even like? [Spock appears at the turbolift door and Uhura walks past him] Kirk:[as he walks past Spock] Ears burning?
Before that, Kirk vents about Spock to Uhura.
Kirk: Sometimes, I just want to rip the [pauses] bangs off his head.
Kirk enlists McCoy to help out Carol with studying one of the torpedoes. So Bones starts flirting with her, knowing that Kirk was listening over their communicators. The entire bridge crew just rolls their eyes.
Kirk: Bones, thanks for helping out. Dr. Marcus asked for the steadiest hands on the ship. McCoy: You know, when I dreamt about being stuck on a deserted planet with a gorgeous woman, there was no torpedo! Kirk: Dr. McCoy, may I remind you that you're not there to flirt. McCoy: [to Carol] So how can these legendary hands help you, Dr. Marcus? Kirk: Bones...
Sulu and Kirk even look at each other with disbelieving "WTF?" looks on their faces when Bones relays his Gorn story.
McCoy: Sweetheart, I once performed an emergency C-section on a pregnant Gorn. Octuplets, and let you tell you, those little bastards bite. I think I can work some magic on your missile.
More of a meta laugh, but consider the fact that McCoy actually performed Rocket Surgery. Multiple times, since they had to repeat the process to remove Khan's crew from the missiles and then activate them.
Carol and Kirk once the latter realizes the former's identity.
Carol: You're much cleverer than your reputation suggests, Captain Kirk. Kirk: I have a reputation?
Then she mentions she heard all about him from Christine Chapel, then after a couple moments talking about her smirks and tells Kirk "You have no idea who I'm talking about, do you?"
When Kirk, Scotty, and Harrison are aboard Vengeance and making their way to the bridge. A random mook appears form round the corner and Harrison immediately goes from talking to beating the guy up. Kirk and Scotty watch for a moment then begin to slowly back away.
Spock questions Kirk's decision to team up with Harrison/Khan to sneak aboard the Vengeance, take down Admiral Marcus, and rescue Scotty.
Kirk: The enemy of my enemy is my friend. Spock: An Arab proverb attributed to a prince who was later betrayed and beheaded by his own people. Kirk: Still, it's a hell of a quote.
When the Enterprise drops out of warp, and Kirk messages Chekov to find out what happened, and says in the most resigned voice ever...
Kirk: Chekov, did you break my ship?
Just about all of Chekov's scenes in engineering count. The guy is running around, often wearing super Adorkable goggles, trying to fix the issue.
When Kirk and Harrison are preparing to jump from the Enterprise's airlock into the Vengeance's, Scotty protests that it would be like "jumping out of a moving car, from a bridge, into your shot glass".
Kirk: It's okay, I've done it before.note Referencing jumping down to the drill in the first movie. [Harrison gives him a weird look] Kirk: Yeah, it was vertical, we jumped out through a...a... (beat) It doesn't matter.
The best part? Judging by Harrison's look, he very possibly thought Kirk really had "jumped out of a moving car, from a bridge, into a shot glass".
It's also the only time in the whole movie where the man doesn't look creepy or evil, which is funny in itself.
And how, after Kirk claims it 'doesn't matter', Harrison simply turns away with a small roll of his eyes.
After Kirk awakens from being healed from near-death through Khan's blood:
Bones: Oh, don't be so melodramatic. You were barely dead.
Bones: Are you feeling homicidal, power-mad, or despotic? Kirk: No more than usual.