The shuttle is about as reliable as a zepelin. Like von Braun said, with the solids it lacks abort modes.

Failure one was caused by an SRB failure. My view: previous o-ring failures had been ignored,
new joint compound was used without adequate testing, engineers' warnings ignored on launch day.
Pressure due to delivery of State of the Union speech may have played some role in poor judgements.

Failure two was caused by a foam strike. My view: non working condition of debris impact monitoring systems was ignored before launch, models of foam debris impact were inadequate, general communication failure after debris was seen strking.
Impending action against Iraq appears to have limited use of inspection systems.
I think that with proper response the crew could have been saved in failure 2.

Now is the shuttle safer as a result of responses to these two failures? The big concern right now is with aging, and I've had a stroke. But I think the way to go is to extend operations for a bit, and get on with Direct, an ISS Orion variant, and man rating the EELVs immediately.

The fix we find ourselves in is because Ares 1 is a dog.