You can get a first flush diverter added to the tank, the first amount of rain which cleans all the crud goes into one section, that you clean out after every rain, then the rest flows into the tank. One was shown on Costa's Odyssey the other night.

In some new developments they properly harvesting rain from the roofs of all the houses to go back into the town water supply. I think in those cases there are issues with people storing water for themselves.