Prior to the hurricane, I don't see any issues.
As of the morning after the hurricane, it should have been clear that this was not an ordinary disaster. FEMA is not equipped to do what needed (and still needs) to be done. That isn't their job. The military should have put in charge of the task on Thursday morning. Instead, General Buchanan was not appointed until the following Thursday. When asked why it took so long to make that appointment, a White House spokesman replied that they didn't need him eight days ago. The spokesman was wrong, and obviously so.
The last part of your question emphasizes the difficulty of getting supplies to where they are needed due to being on an island. That is exactly correct, which is why the emphasis from the beginning should have been on rebuilding rather than resupplying. They should have been shipping bulldozers instead of bottled water. You can't feed three and a half million people by helicopter shipments. You need a functioning infrastructure.
It was clear from day one that people in remote villages simply could not be maintained. For those people, you save their lives, and come up with a plan to get them into urban shelters with running water, and if you can do it, some sort of security to keep their homes from being looted until they can return.
Obviously, I don't know exact details of what ought to be done, and no one does. Somebody ought to, though. The guy in charge should have been given goals to get power into a certain number of cities, and get one or more of those pharmaceutical factories on line. Instead, roads and ports are clogged with small scale diesel deliveries to keep hundreds of thousands of small scale generators going. That is no way to run a modern civilization.