The Problem of Evil (part 1?)

I was thinking about the "Problem of Evil" (POE) last night, while laying in bed trying to go to sleep. I didn't get very far in thinking about it, since I fell asleep really quickly, but I was troubled by something I had heard about it. Apparently, from studies regarding the public perception of the Christian faith, it turns out that the POE is the biggest stumbling block to people believing in the God of the bible. I've also noted this from experience; it seems that I've heard more objections to the Christian faith regarding the POE than anything else.

The POE takes many forms, and lots of people don't even realize they're essentially the same thing. For example, there seems to be a large interest in this question "Why won't God heal amputees?" The idea is that, if God is good and real (ie, if He exists), then He would do miraculous healings of all kinds, not just of the kinds that people would normally recover from (such as sickness or broken bones). Since we don't see any amputees being healed, that must mean that all healing is natural, and probably means that God doesn't exist. After all, wouldn't He want to heal amputees?

This is just a special case of the famous syllogism (I don't know who originally came up with it):

• Premise 1: If God were all good, He would want to eliminate evil.
• Premise 2: If God were all powerful, He would be able to eliminate evil.
• Observation: Evil exists.
• Conclusion: God is either not all good, not all powerful, or neither good nor powerful (but He can't be both good and all powerful).

This syllogism has multiple logical problems with it, of course, but simply pointing out those inconsistencies isn't usually enough to persuade non-believers to accept Jesus Christ as Lord and Savior.

I'll have more on this later, but for now, what are your thoughts on the POE?