I am looking at a place to buy and start a nano-brewery; it has a radon mitigation system. Are there any effects from radon mitigation on the water quality? How will it affect the beer taste and quality?
Radon is a colorless, odorless, tasteless noble gas. So the radon itself will not affect water or beer taste. The mitigation treatments work by bubbling air through the water, or filtering it through charcoal.
And because many homebrewers filter their water through charcoal with no negative affects on water flavor, I assume it will not directly affect beer flavor, although filtering may change your water composition, which may in turn indirectly affect flavor.
As far as beer quality unless the mitigation system reduces the levels of radioactivty to zero (or at least below any limits that may be promulgated by the Environmental Protection Agency (EPA), the Occupational Safety and Health Administration (OSHA), the Food and Drug Administration (FDA), and the U.S. Nuclear Regulatory Commission (USNRC), the Agency for Toxic Substances and Disease Registry (ATSDR), and the National Institute for Occupational Safety and Health (NIOSH), then I would say that yes, beer quality is negatively affected because you making radioactive beer that poses a theoretical health hazard to consumers.
I hope for the sake of your beer drinkers that you consult an expert regarding the safety of putting that water in a packaged food product before you buy that prospective brewery site.