I hear/read a lot about how Kirk was a dumbass for not raising shields earlier and how Khan was a dumbass for not figuring out the "weeks seem like days" code. I don't agree with those assessments.
Kirk: he's been behind a desk for an unspecified number of years. Long enough to be rusty. It was established in TMP that a mere two years of unfamiliarity dulls Kirk's edge. When the Reliant was approaching, even without communications, Kirk kept the shields down because it was a friendly vessel, one of their own. Old school Kirk in season 2 of TOS might very well have smelled something rotten, but this was Rusty Kirk. When he was told of the phaser lock, he had the shields raised. Should he have done it when Spock told him reliant had her shields up seconds earlier? Sure, but again, his reflexes were slower and it was only a matter of seconds. After the battle, Kirk fully realized he dropped the ball big time. Being who he is, he was determined to not have that happen again, and it didn't. He knew exactly how to deal with Khan and from that point on, he played him like a drum, Once he sized up the situation, Kirk slid back into his classic state. He played his bluff, bought some time, then changed the odds. He failed first, learned from his mistake, then got back up and kicked ass. That's what a hero does.
Khan: the thing about movie Khan was that he was totally batshit crazy. His supreme ego wouldn't allow him to accept responsibility for his own predicament. Add the horrific death of his wife and you've got a crazy dude with a revenge obsession. Khan, while being genetically enhanced, was out of his depth and off his game. He only won the first skirmish against Kirk because he was off his game too. Unlike Khan, however, Kirk learned and got back in the zone. Khan was still crazy, still too convinced of his own superiority to suspect a coded trap.
Kirk was no stranger to easily duped adversaries ("but Captain, the Romulans have broken code 2"). Kirk wasn't fighting against Khan in his prime, but Khan after 15 years of insanity and obsession. Nobody in Khan's position would be thinking logically, he was going completely on emotion.
So, no, I don't have these issues with Kirk's lack of reflexes or Khan's intelligence. To me, it was all part of the characters.