5. The danger signals seem obvious now. So what was NASA thinking?
The Columbia Accident Investigation Board has taken great pains to avoid falling into the trap of having 20/20 hindsight because what seems clear now wasn't before the tragedy.
The 1967 Apollo 1 fire is a great example: Pump pressurized pure oxygen into a capsule, lock three guys inside for a day and hope there are no problems with the miles of wiring.
In the case of the Columbia tragedy, no one saw the big picture. The clues were there, but no one realized there was a puzzle to solve in the first place.
First, the external tank was designed with a layer of insulation foam that isn't supposed to shed during launch. It was designed to stick to the tank, so if it's not sticking then something isn't working the way it's supposed to be.
Second, the shuttle's heatshield of tiles, RCC panels and thermal blankets were not designed to be damaged in any way for any reason. That's why the orbiter isn't allowed to fly through rain, stay outside when it hails or risk having workers drop tools on it. The tiles are especially fragile.