In the Director's Cut, Kirk decides to have a little fun at Midshipman Preston's remark that the Admiral will find everything "ship-shape".
Kirk: Oh, do you? Do you have any idea, Midshipman Preston, how many times I have had to listen to Mr. Scott on the comm, telling me his trouble? Do you have any idea of the ribbing I've had to endure in the officers' mess... to the effect that the Enterprise is a flying death trap?
Preston: Oh, no sir! Wha... this is the finest engine room in the whole Starfleet! If the Admiral can't see the facts for himself, then, with all due respect, he's as blind as a Tiberian bat!
Scotty introduces him as "my sister's youngest, Admiral", but the reading makes it sound like "my sister's youngest Admiral", which is apropos since Preston seems to think he's the Admiral.
The scene where Spock has Saavik pilot the Enterprise out of spacedock. Kirk is trying his level-best not to be scared out of his wits by the fact Spock is making her do it without any prior experience.
McCoy: Would you like a tranquilizer?
[Kirk quickly shakes his head]
The funniest part is Mr. Unemotional is clearly being a Troll. The most external reaction is Spock raising one eyebrow, but you can tell he's giggling in his head.
After Saavik nails it and successfully pilots the ship out, he smiles and shrugs to Bones as if he had no doubts in her abilities all along. Bones' expression is silently calling bullshit.
When they share a turbolift, Saavik is utterly oblivious to Kirk's attempts at flirting. Followed by McCoy (who's been waiting for the lift) snapping, "Who's been holding up the damn elevator?"
Kirk: I would not presume to debate you. Spock:[half smirk] That is wise.
When Kirk is climbing down the levels with Spock on the way to the bridge, Kirk tells him, "That young man there. That's my son!" Spock replies in the most bored tone of voice, "Fascinating." For an unemotional being, Spock is certainly expressing his non-interest in a very emotional way!
One could also read plenty of sarcasm into Spock's reply, too. As if to say, "You sleep around so much, of course you'd eventually come upon a son."
Kirk's observation that for all of Khan's self-supposed superiority, repeatedly playing a Batman Gambit with him by hitting his Berserk Button is reliably easy:
Kirk: I'll give him this: he's consistent!
When the Reliant goes into the nebula, Joachim sensibly orders a reduction in speed (glaring right at Khan to hit home that charging after the Enterprise is a bad idea). Khan instinctively turns to rage at him, but, knowing Joachim is right, manages to rein himself in and keep quiet.