As I stated in the original post and you agreed with above, state and local authorities failed in numerous of their responsibilities. Once on scene to verify those failures, FEMA's execution of its responsibilities needed to be at a higher level in order avoid being seen as just another level of government that was not providing relief for those that were in need. I did not say that the feds "did wrong", only that their execution had "shortcomings" that allowed them to be perceived as part of the problem rather than part of the solution.
As far as "exactly" what was wrong, I would tend more towards the political part of the fed/FEMA approach and not the actual direct efforts that were made to alleviate suffering and begin recovery operations. By political, I mean making certain that every media outlet was fully briefed on the state/local responsibilities that were not executed and how the feds were trying to pick up that slack as well as execute on actual federal responsibiities.
Further on the political front, the "good job, Brownie" comment was either from a lack of knowledge or deliberate false reporting of situation status to the President. I will allow that it also may have come from Bush's Texas good-ole-boy approach to politics.