Unlike Scrivener [via IHE], I don't really think that Bush is dumb in a straightforward intellectual sense. Odds are good he's as smart as I am, and in some ways (like remembering people's names and faces) he's probably considerably higher on the scale. Whether it's his ability to pick people or innate, he's a damned sight better at political strategy than I am (though, to be fair, I've never really been put to the test, as nobody has ever taken my political advice in an actual competitive campaign).
What he lacks is, in my view, two crucial things: empathy and compassion, a really strong moral sense, but that's not the issue here*, at least I don't think it is; and the sense that bad things can happen. Foresight, and the understanding that "risk" means that sometimes things go wrong, seems to be entirely lacking from the politics and policies of this administration. "No one could have foreseen..." is, as Scrivener and others have noted, flat out wrong, in addition to being prima facie evidence of the administration's failure to consider accident and failure as possibilities.
The entire Iraq war and reconstruction has been a whole series of high-risk policies which failed to go as planned, resulting in embarrassing retrenchments and redirections, not to mention unnecessary human suffering in the present and foreseeable (if you do that sort of thing) future. New Orleans was a high-risk city: everyone who seriously calculated the odds knew that disaster was a matter of time. New Orleans' great charm is not its luck, but its sang froid in the face of the inevitable. New Orleans is not a city of wishers and hopers, like our administration: it's a city of people who live in the past and present like there is no tomorrow. It would be an insult to the city to say that we have a New Orleans kind of president, because he insists on making plans for others, instead of living life for himself.
* Though, as Anne Zook says, "'Incestuous nepotism' doesn't even begin to describe these people and the inbreeding is producing some monstrous results." Though it would be somewhat hypocritical for Congress to impeach as incompetent cabinet members and agency directors they already confirmed, it's hypocrisy even I can live with. Repudiating the sins of the past is the right kind of hypocrisy. But they must redeem themselves: we can't do it for them.