Top FIVE dumbest mistakes:
Apollo-1 fire. 100% oxygen atmosphere, at 15 PSI, very dangerous.
Launch of Soyuz-1 despite engineers saying it was not ready.
Soyuz-11 crew died preparing for re-entry as a valve opened that was not supposed to until below 10,000 feet.
Launch of Challenger despite engineers saying it was too cold.
Refusal to allow engineers to use CIA spysat assets to look for damage to Columbia on STS-107 (as WAS done for STS-1 in 1981!). If they'd been allowed, the the leading edge damage would have been discovered and a decent chance of a rescue mission to save the crew (next shuttle mission was already mostly stacked and could have been made ready in time).
I'm not including the "Nedelin Disaster", killing at least 78 (fittingly including Nedelin who foolishly required ground crews to try to fix a fully fueled missile, rather than wait a day to drain it, as he sat in a chair at the pad and the second stage accidentally ignited. Also the missile was not really designed for draining very easily). Because that was a military missile disaster and not "Space Exploration" by any means.