Why was the russian invasion such a huge mistake?

They got beaten, yeah, but the russians brought two armies to eastern prussia much faster than the german general staff deemed it possible and this lead to the decision to relocate two corps from the west to the east, which missed both the battles in the east and the first battle of the marne in the west, maybe even tipping the scales in favor of the french and british.

Maybe we should provide a definition of a "grave military mistake", and where blame for "worst mistake" is due and where the defeat was rather a result of bad luck, fog of war or a decision which seemed reasonable at the time but has been declared wrong by hindsight.