If the standing law established by your elected representatives poses no bar to that action, then it would be theoretically permissible according to the law.

It would of course be a foolish thing to do given the risk of a lawsuit (the cost of which would probably exceed the alternative cost of proper toxic disposal).

Essentially, you are asking the question about how to deal with negative externalities. Such issues affect all political systems in various ways, not just libertarian theory. Heavily regulated markets under democratic governments are apparently incapable of dealing with a similar effect known as the 'tragedy of the commons'.

Essentially, the flaw is in our legal structure and our eonomic system that places no material value on non-market elements. This is a problem whether one approaches the issue from a libertarian perspective or an authoritarian statist perspective. The problem is not the perspective of approach, but the integral market failure to price non-market goods (fresh air or fish in the oceans).