From Mormon Metaphysics:
Someone asked at LDS-Phil about the problem of evil. This is my (swiftly written) answer. My apologies for any grammatical errors or typoes. I don’t have a lot of time to write at the moment. But some might find this interesting.
I think you have to separate out the problem of evil into two parts. One is the logical problem of evil. Then there is a different question with different names but which I tend to call the evidentiary problem of evil.
For the former the LDS notion rejection of creation ex nihlo allows a Mormon to respond that God is limited (since things exist independent of him, and he may even have limited power over them). If God is limited one can respond that evil must logically exist simply because God can’t do anything to totally eliminate it. Often LDS theodicities take different tracks explaining why. The typical, although not universal, approach is to say that intelligences are (in some sense) free and that God can’t totally take away their free will. Thus they can always choose evil and God can’t do anything about this. This ends up following to a degree one popular response to the problem of evil by mainstream Christian philosophers but with the added strength of LDS finitism. (Roughly the idea that intelligences are uncreated and free)
The evidentiary problem of evil is different since it asks not why there is any evil at all but rather why there are these evils. Thus one could ask why God allows child abuse, destructive hurricanes and so forth. I personally find most responses to this question much more problematic and weak. But I think that overall the LDS position still ends up being stronger than most theistic answers.
One popular view (probably best formalized by Nate Oman as I recall) is the issue of contract. That is since each of us chose to come to this planet knowing all the possibilities we can’t blame God for the evils we do experience since we freely chose to experience them. Thus the LDS plan of salvation and council in heaven resolves the problem - to a point.