With Chris Busby’s discovery of large amounts of uranium in a Tokyo air conditioning filter, and the detection of uranium in sardines caught off the Japanese coast, it is likely that uranium and its radon daughter products are contaminating many tap water systems in the US. This is in addition to naturally occurring radon in the water.
Reverse osmosis systems are a popular method for purifying water in homes. These system usually utilize 2 or 3 GAC (activated carbon) filters to remove gases like chlorine. They are also an efficient way to remove radon from tap water.
According to this pdf from the Maine radiation control program, radioactive lead-210, a long-lived isotope, accumulates in the filter. Eventually it is considered to be nuclear waste. The filter may still be operating at high efficiency, but external radiation will be emitted from it, causing a health hazard.
The filters should be changed frequently, or shielding like bricks or lead foil should be placed around the RO system to block the gamma radiation.