@Didymos Thomas,
ArthBH,
One thing to note is that the matters of God being omnipotent, omniscient, etc. rest entirely on your conception of God. Is God a meddling God, a causal God, a removed God, etc? Perhaps the most important underlying point may be how relative God actually is, or at least the conception of it at any rate.
What if God were not involved in the affairs of the universe? Aristotle supposed that God was an "unmoved mover" which was a purely actual (paronymous) being that could be nothing else except what it is, the prima substantia which all other substances rely on, the origin first movement (but not of movement itself). God is very much removed from the universe except in the nature of first cause. Much similar to that is Rene Descartes who would say that God set things in motion at creation. I wonder if it could be argued that if things were set at creation, then it is part of a perfect plan to being with.
So on that note, what if God's initial plan incorporated bad elements, would that make it less perfect if it were part of an overall perfect plan? Leibniz would say that the universe is reflected in Monads. Even in that, God created all possible instances in a plurality of monads at the creation of the universe, reflected only in the dominant monad, which itself relied on the principle of pre-established harmony (allows the universe to run without supernatural intervention). God's conception of the universe, time, etc. was perfectly laid out and revealed only in the reflection of the dominant monad.
Suffice to say that God could exist in a world of constant troubles, if anything because we could think of God as something wholly primary.