the Kobayashi Maru sequence
Was terrible. Instead of it portraying how badly Kirk doesn't believe in no win scenarios, it was basically him acting like a punk and sticking it to Starfleet.
How much exposition do you need, and when exactly do you need it? Before the test, McCoy and Kirk had a brief discussion about him taking the test a third time, with Kirk asking "Doesn't it bother you no one's ever passed the test?" and McCoy saying "No one passes it much less takes it multiple times", with an implied "you lunatic". Then during the trial shortly after the test where Star Fleet accuses Kirk of cheating, he said directly "I don't believe in no-win scenarios" and expressed his opinion that the test itself was the cheat.
As for the test itself, Kirk's behavior was perfectly believable for the 20-something cadet, and it was hilarious, as were the reactions of his crew. While everyone was exasperated with him, especially his crew, he expressed his exasperation with the test by showing his contempt for it by going rogue, making a farce of it, and winning the purposely unwinnable test. Yet despite his insubordination, by the end of the movie, he's awarded a medal and the Enterprise, and he's earned the respect and trust of his crew. IOW, he's Captain frickin' Kirk.