It has nothing to do with Rudy Giuliani's "broken window" approach to restoring civilization to NYC (which is no fallacy - it worked well, because providing latitude in the little things, filth, petty crimes, bums and addicts sleeping in parks, hostile squeegee men, etc. implicitly endorses latitude in bigger things, leading to an atmosphere of anarchy that nobody wants to experience).
The excellent Bastiat QQQ yesterday brought it to mind. Bastiat's famous parable of the Broken Window explains how a kid breaking a window, despite the expenditures to repair it, on the bottom line does no favor to the village's economy.
While some Keynesians might argue otherwise, I would make the case that, although maintenance of things we care about is a large part of an economy - cars, houses, boats, gardens, horses, dogs, bodies, etc - the fallacy there is the failure to reckon the opportunity cost of the money on the part of the window-owner.
I recently posted on the subject of the pseudo-rationality that ensues when the costs of an event are calculated, but is not compared to the costs of inaction or of alternate actions - or the advantages thereof.
If anyone were to calculate the global economic advantages of global warming, for example, I think everyone would be praying for it - but I doubt it will occur in any meaningful way.