All failures of management
Aside from all happening in the winter, NASA's three big failures all have something else in common, fundamentally they were all failures of management.
Apollo 1 happened because NASA management let quality control and oversight slip and put the schedule ahead of everything else. This resulted in North American delivering the block 1 Apollos in such a shoddy state that they were basically death traps.
Challenger's management failures are already well understood and are used to this day as a case study in how not to manage high risk projects. Management had ridiculously optimistic estimates of the risk of operating a shuttle which, as Richard Feynman noted, would mean that you could launch a shuttle daily for 300 years and expect not to have an accident if true, a figure that was blatantly ridiculous to even the rankest layman and which flew in the face of NASA's own engineers who put the risk of failure at 1 in 200 (which while still optimistic as it turned out, was far closer to reality than Management's figure). It seems they were in the habit of minimising risks and ignoring engineers and when the engineers raised concerns over the Challenger flight they were ignored once again, but this round of Russian Roulette was one round too many.
It's disheartening to know that Management made almost the same mistakes with the Columbia disaster. Once again, Management started minimising known risks for the sake of the schedule, ignoring repeated incidents where the heat shield was damaged by shedding tank foam, treating the incidents as annoyances rather than life-threatening events. Once again, engineers raised concerns that the heat shield had been damaged and wanted to plan some contingencies, and again they were ignored. And while a rescue was unlikely there could have been options if only the engineers had been allowed to formulate and execute a rescue mission of some sort.
On the other hand, arguably NASA's biggest success, the safe return of the Apollo 13 crew, was largely down to superlatively good management. Managers and engineers pulled together and worked through the problems one by one and the end result was three exhausted and traumatised, but alive, astronauts standing on the deck of the USS Iowa Jima.
NASA needs to learn the lessons all of these events have to teach and learn them properly. Until they do they'll simply be waiting for the next disaster.