"Trailings" was almost certainly a typo (shame on the Atlantic Monthly) - the correct term here is "tailings."

On site at many mines are large tailings piles, which are the rocks, dirt, and such that are cast aside as valueless during the mining process. In some cases these piles are made into great big, flat-topped slabs - they look like mountains with their tops sliced off with a razor, they're so flat. If any of you have ever flown into Tucson, AZ, you've seen them out the window - odd, flat mesas that look far too large to be made by humans, but sadly are.

Because tailings often have traces of whatever metals are being mined, runoff from rain that lands on and trickles through a tailings pile is often heavily contaminated - this is the source of much of of the water contamination at mining sites, and probably why it would be mentioned in an article about Superfund (which we at EPA abbreviate $F).

I'd agree with the distinction you make - tailings are the stuff that gets cast aside immediately, slag is the stuff that is left over after you refine the ore to get the valuable stuff out.