I'm sure the pundits will have a field day dissecting Cook's tactics, but I don't think he has any questions to answer.
Clearly the follow on wasn't enforced because he didn't thing the score was big enough.
He batted on as long as he did for the same reason, winning the mind games by setting a total that was out of reach.
To keep that total out of reach he set what some might argue were negative fields, but there were no complaints from his bowlers. It actually showed great confidence in them being able to strangle the opposition out.
England have already won one test against NZ with a tremendous attacking bowling effort, but there are days when this won't come off.
Getting some practice in at working hard and chipping away is vital with the Ashes looming. You need a diverse arsenal at your disposal to win the longer series, and that weaponry needs to be honed to perfection.
When Australia were the dominant cricket force they time and again won from positions that seemed impossible. This England team is showing signs of being able to do that too. I think Cook is a canny skipper. Finding different ways to win is vital. Having experience in executing them is priceless.