The problem of Evil ultimately is a question raised based on morality. It evaporates as an objection by the athiest, as the atheist doesn't believe an objective moral standard exists to judge evil from that which is morally good.
However, for the purpose of this discussion I will evaluate the question of... "Why does what is evil according to the Judeo-Christian tradition take place, of God is all-loving, all-knowing, and all-powerful?" As that is generally how people actually mean to ask the question.
So why do nature-induced evils occur? First we must decide what exactly is a nature-induced evil. Since this is in evaluation of the Judeo-Christian world view, I would say most of what you have listed isn't actually morally evil.
So far the only two that could possibly be tied to a moral evil, would be Birth Defects(miscarriage would be part of that) and Plagues. The only reason why this might be morally evil, is that people die. However, death itself is not declared to be morally evil in the bible. If it did, we would all be in trouble. The only thing death-relate that is proclaimed to be immorla (whether you agree or not with the bible) is murder. Murder being the unjustified killing of another human being.
So the way you have asked it, should really be renamed, "The Problem of Suffering."
So why does nature-induced suffering occur?
YouTube - Since Evil & Suffering Exist, A Loving God Cannot ...? <--- Human induced evil/suffering
Ultimately, the existance of nature-induced suffering isn't a moral question, but rather a question of personal convenience. You can not morally condemn something by a moral system you philosophically deny.
I hope I have addressed this somewhat satisfactorally.