Is air pollution bad, or isn't it? If you were to walk up to any person of average economic learning (the average is pretty low, remember), they would say "Well, of COURSE air pollution is bad." That's a natural consequence of the question. Now ask the question this way: "Is polluting your air bad?" and you will get a different answer from a thoughtful person.
This latter question presumes that air can be owned. Does it make sense to talk about ownership of air? Nobody seriously thinks about ownership of air because there is no way to control the flow of air. Air is ordinarily fungible -- one bit of air is just like another. If the wind is blowing one way one day, and you give me a certain quality of air, then when then wind blows the other day, it only seems fair that I should return your air in the same condition I got it, right? Otherwise you should have a private right of action for redress.
Certainly the current system, wherein "We all own the air", produces sub-optimal uses of air. In an effort to control abuse of air, "we" have set rules that allow for controlled amounts of pollution. This bothers some people, because they put a higher value on clean air than do others of "us". This is a problem in a democracy, of course, because whenever you vote, some win, and some lose. Anybody who doesn't like the current levels of pollution has obviously lost. Anybody who is polluting underneath those levels is not doing anything wrong, in *any* sense of the word.
Private property rights lead to a different system for regulating air pollution. Therein, you would expect that the quality of the air flowing over your property's borders was identical no matter the direction of the wind. If it differed, then you would expect to be compensated by the upwind property owner.
Exactly how that would turn into a system of payments would depend largely upon the businesses that people create and the available technology. For example, it's very likely that you would rent the air pollution rights to your property to a local holding company. That company would monitor the air quality as needed around the neighborhood, and send out bills to transgressors. If there weren't many transgressors, then you would probably end up having to pay the local holding company.
Now, you might say "But that's horrible! Why should I have to pay for clean air?" You pay taxes now, right? And those taxes pay for the EPA, right? You're paying for clean air now. Do you feel like you're getting your money's worth? Would you pay more taxes if you knew that would actually result in cleaner air? Some would, and some wouldn't. That's how free markets work. You pays your money and you makes your choice. Freedom results in more people getting exactly what they want, and everybody getting more of what they want more than our current fiat system of air pollution control.