You indicated that you don't believe that there is any such thing as common property. I'm hoping that you are rethinking that regarding something like a county court house.
As to Air...
Air is not common property; it is not the property of society; it is not owned collectively. It is simply unowned. That does not mean, however, that it can be used as a vehicle to violate other people's rights by, for example, transmitting harmful pollution onto an unwilling individual or his property. Air wouldn't be the property anyway, since property, properly understood, are those rights (all of which are actions) that one has the moral sanction to pursue relative to the object in question.
If I created some 'air' in my laboratory by mixing gases, then clearly I'd have the moral right to dispose of it, use it, etc. (And, as you say, none of these rights could ever include the right to violate someone else's rights.) But is this different from having any rights in the air that circulates around and past my house?
I think that there are some differences, but not as many as one might first think. I can bottle the air around me and even though I didn't create it, I have acquired a right to sell it (done everyday in those gas stations that have coin-operated air pumps, and at SCUBA shops). I have the right to breath air no matter where I am standing (I might not have the right to stand in some places, but I don't see how I could not have the right to breath air, even if I'm trespassing).
With what you are calling "unowned air" I have a moral and legal right to modify the physical and chemical make up of the air, but only to the degree that it isn't infringing on the rights of others to use the air in various ways. (With every breath I take, as the song goes, I keep some oxygen and increase the Carbon Dioxide, whether others like that or not). If I put a tiny bit of pollutants in the air, it won't violate the rights of others. If I put a lot of pollutants in the air, it will. My point here is that to have some moral rights in air, is to have some degree of ownership. If it isn't air I created in a laboratory or factory, then it is air that, to the extent that there can be any ownership - i.e., rights, then it must be a common ownership.
For water, I'd refer you to Riparian Rights. These are legal rights that in the U.S. mostly come to us from English Common law. They attach certain rights (actions: e.g., boating, fishing, swimming, drinking, etc.) to the control and use of the water as is passes through a piece of land to the owner of that land. They define rights, but the main purpose is to limit the rights of one landowner such that he can not deprive the landowners downstream of their riparian rights. It is a common property (common set of rights) but limited to those that own land adjoining the water in question.
There are other rights that are common, not to all citizens, but to the owner (or perhaps controller) of a piece of land. Like the mineral rights, or the right of passage in the sky over the property - air space rights.
I believe that we need clear legal descriptions - that is legal rights - to let us have a civil society and settle disputes according to rational, objective law, and to be able to plan in ways that minimize conflicts and predict outcomes. These laws must include all those things that can have the effects on us that land, water and air have.
Law should just be made up willy-nilly as to what sounds good. It must be logically derived from moral rights. And the moral rights that pertain to a class of objects must be derived from the more abstract and general rights. Man's right to his life is the source of all the rights that follow - right down to who has the right to jump in a creek and go for a swim.
From that perspective, I'd say that if there are two people and they are in potential conflict over the same object, that object is subject to moral rights as property (a bundle of rights defining moral sanction to various actions regarding that object or class of objects). If there are two people and an object, it can never be totally unowned (e.g., without sanctioned actions that apply to it).