helped fund efforts to undo a model diversity policy in the Wake County school system in North Carolina, effectively resegregating the district – part of a larger campaign, the film alleges, to weaken the public school system and prepare the way for widespread privatization;
pushed voter ID laws – purportedly aimed at combating ballot fraud but really designed to keep Democrats from voting – through their financial support for the American Legislative Exchange Council, an increasingly radioactive business group specializing in the drafting of corporate-friendly pick-up-and-pass legislation for state lawmakers. (ALEC is also behind the insane "Stand Your Ground" gun laws at issue in the Trayvon Martin shooting case);
pumped millions of dollars into more than 150 colleges and university in exchange for control over hiring and curriculum decisions, to ensure students will be exposed to the free-market fundamentalism of Ayn Rand, Freidrich von Hayek and like minds;
bankrolled a coordinated campaign to swing public opinion in favor of privatizing Social Security, deploying Koch-funded think tanks, experts, and pundits to spread the myth that the program is on the brink of bankruptcy.
(Greenwald might equally well have documented Koch-funded efforts to repeal Obama's health care law, deny climate change, undermine collective-bargaining rights, or block Wall Street reform, but there's only so much a single film can cover.)
All diabolical stuff, from the liberal point of view. Of course, you might want to argue that even if the scale of the Kochs' doings puts them in a league of their own, they're just exercising their constitutional right to play politics at the platinum level, like plenty of other high rollers on the right (and on the left, for that matter).