Spock nerve-pinching the punk on the bus who wouldn't turn down his boombox and flipped Kirk and Spock off when Kirk told the punk to turn off his music. He even receives a round of applause by the other passengers. And everyone in the theater when this movie came out in 1986.
This little dialogue is a real zinger.
Spock: To hunt a race to extinction is not logical.
Gillian: Whoever said the human race is logical?
Early on in the sequence at the hospital, McCoy comes across a woman in a bed receiving kidney dialysis. He remarks on the 'dark ages' of medicine he's in, then gives her a pill to take. Later, during their escape, an utterly baffled group of hospital staff are standing around the woman, now in a wheelchair and looking quite lively. The United Federation of Planets' medical science is amazing.
After watching everyone else struggling, pulling favours, and outright bribing to get the supplies they need, Sulu just shows up flying a helicopter. One that he just learned to pilot that morning. No explanation given as to how he convinced owners to let him take it out. None needed, he's just that badass.
Gillian's last confrontation with her boss.
Gillian: You sent them away without even letting me say goodbye to them!
Gillian[slapping him]: You son of a bitch!
The still-cloaked Bounty interposing itself between the whaling vessel and their target, causing the harpoon to clang off their hull. Then they decloak, and the whalers freak out trying to get away.
Kirk and company pleading guilty at their court martial. There's no bluster or demands for special treatment despite them having just saved the lives of the President, the Federation Council, hell the entire planet. They know they did the right thing, but are still willing to face up to the consequences fo the their actions.