The quality of water is influenced by atmospheric components like the aerosol contents etc. Is it necessary to purify the rainwater in order to use for domestic and drinking purposes?
Rain water harvest is becoming popular in different part of the world especially where there is shortage of groundwater. People harvest rainwater if the groundwater is contaminated with arsenic. I think it is necessary to monitor the quality of rainwater.
Depending on how clean and maintained is your catchments and tanks .. although it is naturally distilled .. but several pollutants may end up in your harvested water .. it may need filteration .. and softner might be needed ..
This depends on how much air pollution there is. For example, air may be contaminated with some chemical elements in urban areas. On the contrary, the air is cleaner in rural areas.
In any case, one can simply analyze some rainwater samples to determine whether they are safe to drink or not.
Well, in urban areas the pollution is higher. Rural areas where there are power stations that burn fossil fuel in huge quantities in those areas rainwater quality should be monitored properly.
The catchment and collection system will dictate the degree of purification required. If the water is used for agricultural purposes or household purposes such as washing clothes, then provided there are no major toxic elements such as As present it may be OK. For drinking and cooking purposes it may still be necessary to purify the water - mostly mechanical type of filtration followed by ion-exchange as necessary.