We had a fairly standard asphalt shingle roof, about thirty years old. It was just torn off and replaced. The tear-off generated lots and lots of debris in the yard and garden beds, particularly since they used a blower to clear gutters, etc. They picked up all the large debris, but all the fine, sand and small gravel sized particles are coating the garden beds.
This is another situation where you likely have collected all the debris you can without seiving out your soil. I am pretty sure the worst part of the asphalt shingle is the asphalt; the parts that are most likely to rub off are the tiny rock particulates that coat the surface of the shingle to protect the asphalt and underlay from UV exposure.
In a similar situation (our old garage roof was blown to pieces into our back yard at my parents' house), I piled on the woodchips, made mushroom slurries and applied finished compost and compost extracts. Any heavy metal pollution will be sequestered in the fruiting bodies of the mushrooms, and other contaminants will be broken down and redistributed by the mycelial network to places they are needed.
The tiny particulates aren't leaving your property unless you go to extreme (and probably very harmful) measures, so I think the best course forward would be to boost the vitality of the soil through the methods I mentioned above, and let the soil life break everything down. If you are concerned about specific contaminants or spots, perhaps consider growing sequestration crops that you then use as mulch somewhere you don't grow food, like a wood lot.
But don't worry. That won't do anything.
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Since you don't mention any of the actual shingles being found, and you have removed as much of the "litter" as possible, I wouldn't worry.
Those little rocks from the shingles may even have minerals in them that your soil organisms (and plants) can make use of.
Many times that "gravel" is ground up granite or other igneous rock, which can actually be a benefit to your soil, microbes and plants.
All of this discussion makes sense but I spent a summer doing garden and landscape maintenance and one house had 4 tall Inkberry shrubs spaced across the front about 25 feet apart. The two on either side of the front door and the hollies between were lush and healthy. The two on the outside corners in front of the downspouts were sickly and hollow. I observed a pile of asphalt "silt" from the roof on the ground under those two shrubs. I don't know for sure if the asphalt was the cause but I extended their downspouts beyond the shrubs and am careful not to expose my own landscaping to anything asphalt. You just reminded me that it's been 3 years and I forgot to go back and see if the shrubs recovered :)
Good observations Susan, Down spouts are going to locally isolate anything that comes down from the gutters.
Acidic rains will leach the tars from asphalt shingles and that is going to stay near the exit of the downspout pipe, it sticks to the soil particles and that seals out air.
If roots can't breathe they start dying and if you add to that the poisonous effects of the components of tars then you have a soil disaster for any organisms in that area.
If you mow the lawn with a riding lawn mower that has inflated tires or use a wheel barrow with same you can swing a big magnet over the lawn to pick up the hidden nails. There is also a wheel device that has magnets mounted between two wheels that you push. This item may be rented in your area.
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