When metal objects accidentally make it into the dryer they scratch off the epoxy coating and expose the metal, and when wet clothes sit on these scratches rust occurs.
Either you have something in the dryer that is rusted and rubbing off on the clothes or it is coming from the washer. There might be rust in the water.
Some how mositure or a substance is in your dryer . Get in there with a cloth and check it out to make sure you do not find somthing that is causeing the rust substance. Clear if off. If you put a belt in the dryer or something metal this could be the problem too .
If iron in your water caused the rust stains, try Iron Out (warning: smells like sulfur). If it's iron, do not use bleach; it'll set the stains. Some liquid softeners can cause stains, too. Of course, it could be your dryer. :)