What went wrong in the case of Al-Zarqawi

Well, first of all, it is good to see this murderous man dead, but the US also killed two women, a child and a man with their most favorite weapon to date, the bomb.

Since the new age (and perhaps since WW II), the US favors Airstrikes over most other means to attack. It is safe for their own personal and mostly has devastating effects, because a man runs slower than a bomb falls!
Gulf War I was fought almost without other means, like deploying troops and tanks, instead they used continouus airstirkes and other means of mass destruction (carpet bombing (also by plain, but different from a precise airstrike)). The only other weapon used frequently are ground to ground missile batteries, either from Ship to land or from missile bases.

However, what they lack in precision, those bombs make up in devastating explosions and this is also the moral problem with those means and especially in the Al-Zarqawi case.
As I understand it, the US good a hint from the inner circle around the Al-Kaida boss about his whereabouts.
They then send out a couple of F-16 to do the dirty work without respect to any of the innocent persons, who were qualified as valid targets by one common link. They lived next to an evil man.
Does this link alone morally allow an area attack on a feared terrorist boss?

I don't think so, because the US is a powerful nation, which has a lot of options at their disposal.
Even if it is a matter of time, it would have been no problem to send a squad of Marines or Delta Forces with a Black Hawk or similar helicopter and take him. They could have even send one of their favorite drones to scout the area and follow Al-Zarqawi if he tries to flee the scene. It has been done with one of Aideed's henchmen in Somalia and worked out quite well.
So, why the necessity to blow up the whole building?

It seems to be that the US military has long lost regard for the Iraqi people and their lives, seeing them as somehow not so important humans. It is a natural thing for military types, when they are in a all-around-the-clock combat situation with the threat of sudden suicide attacks at every corner. I don't blame them, they just try to do their job.

The problem lies with the order, which most likely had to be approved by either the Department of Defense or the President/Vice-President himself. So, in the end, it was either Bush's or one of his underling's decision and they had the chance to look at it from an objective distance! They failed and not only the people of the US, but also as a protectorate of the Iraqi government!