The rule of thumb that I've always heard is to let the rain fall a good 15 minutes before collecting rainwater. 15 minutes allows the rain to clear the dust out of the air and pound contaminates off your roof and onto the ground.
Yes, and if rainwater is to be regularly harvested, automatic devices are available or can be made to divert the initial roof run off to waste before sending the subsequent cleaner water to a tank or drum.
The usual technique is that the first flow of water fills a bucket or small drum, and that the weight of this vessel when full operates a pivot and thereby diverts subsequent flow into the tank.
The small vessel should preferably have a very small hole in it so that it will slowly empty and be available for the next rainfall.