What happens if Company A contains the pollution on their land, then goes out of business and liquidates their assets to their shareholders who pass them on through inheritance once or twice before the pollution leaks into neighboring land?
Libertarian thinking puts a lot of emphasis on the concept of absolute private property, but it also puts a lot of emphasis in the notion of absolute personal responsibility. Therefore, in a libertarian society there is no such thing as corporate personhood shielding shareholders. A corporation is just a public name, but the responsibility is fully over the individual humans beings enabling the acts done under its name.
Therefore, as long as individual A owns property X, he is fully responsible for whatever X causes to the properties of individuals B, C, D... Does he came to own it through inheritance? Does he want to not be held hostage to the ill effects X will cause down the line? Well, better the move to reduce or eliminate the danger X, lest him, or his sons etc., feel the effects of neglect.
What if the pollution is carbon dioxide and the polluters will fight you in court to your death that it's not a pollutant at all?
Private property is absolute in libertarian thinking, and thus it doesn't matter whether what A is dumping in B's property is. It could be gold bars and diamonds, were B to sue A for violation of property, B would win because A was violating B's property.
Therefore, is A dumping carbon dioxide in B's property? If so, has B signed a contract with A allowing A to do so? No? Then it doesn't matter, A is violating B's property, and will lose. Whether carbon dioxide is harmful or harmless would be strictly irrelevant.
And since A knows he will lose no matter what, he'd know to either get B's approval through a signed contract, or to simply not take chances and not dump anything at all, no matter what.
What if the pollutant is CFLs and you can't prove its harming you since the ozone hole is over the Antarctic where no one (permanently) lives or owns property?
I know this is far fetched, and probably unrealistic, but in theory the polluter would still be responsible for the increase in UV radiation over everyone's property, who in turn would be able to sue him for this increased UV radiation. All the shareholders and decision makers in the company would end up bankrupt very, very quickly.
Libertarianism is failure as soon as you bring it into the real world, no better than communism was.
Wait, that's a stretch. Libertarianism can not make much sense if taken literally, but at least it is pretty clear in that no one can go around gullaging others. In other words, if put into practice libertarianism would probably lead to lots of social ills ("you're free to starve" etc.), but comparing those to communism's ills and saying it is no better is clearly an exaggeration. It might not be good, but better than communism it most certainly is.