Hope this helps
I would want to know what it is filled with, regardless of the current condition.
Most fills have records and info in the town where that are located.
I would contact a local real estate professional to help with this answer and to save time and money.
(I'm on the Cape, but I can help you choose a local pro if you want help doing so.)
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I am certainly no expert but 1 mile is pretty far. If the landfill is owned by the town, I am sure there are some sort of yearly monitoring reports that are available either by the town or state. At the very least have the water tested during your home inspection period.
I found this article: http://www.sixwise.com/newsletters/06/09/29/how-dangerous-is
Nothing is definitive in this article and does bring up the same points that I do which is toxins in the air and ground water contamination.