Well, just to add an alternative view to all this, you probably won't ever hear any of these theological arguments coming up in Muslim circles. No, it isn't because we'd kill all the infidels, though we have some in our ranks who probably would. Rather, good and evil, everywhere I have ever read the matter discussed in Islamic circles, simply refers to those things which benefit and those things which harm, respectively. Therefore, actions typically have both good and evil in them, and one must evaluate actions by balancing the benefit and harm within them. The greatest harm is the hellfire, and the greatest benefit is paradise. A Muslim should live his life attempting to maximize the benefits and minimize the harms, then trust in Allah to spare him that greatest harm and grant him that greatest benefit.
A side effect of this worldview is that some things which may seem evil because of the perceived harm, may have a hidden benefit. Muslims believe in the unseen. The Qur'an tells us that we may detest a thing which is actually good for us. This even applies to death and disease. We pray for good in this world and the next, but we'll sacrifice the good of this world for the next if that is the choice which must be made. This is difficult, and often we come short, but that is the objective. I think the problem of evil is really just caused by a poor definition of good and evil.
The Muslims in the days of the Messenger of God(SAW) regarding the treaty between the Muslims and the Quraysh as evil, and they wondered why they should offer peace to people who oppressed them and tried to kill them and the Prophet(SAW) himself. They only saw the material, immediate harm without seeing the benefit to them, both materially, long term, and in the hereafter. At the time the ummah was small, and they could not understand that which the Prophet(SAW) understood. They saw a few hundred believers among over a million Arabs. Now, this (as it was perceived by many at the time) "evil" was actually a tremendous good for the Muslims, allowing them to make pilgrimages without being stopped, allowing visitors to freely visit the Prophet (SAW), and allowing the Muslims to spread Islam to the point that Mecca was later conquered (after the Quraysh broke the treaty) without bloodshed. Even their suffering had benefit, as it allowed others to see the sincerity of the Muslims.
In order for us even to consider the problem of evil, we really must possess the understanding to define the terms in the problem. It appears to me plainly that we do not. Beings which only have good knowledge of the seen (and that knowledge is obviously incomplete), and very limited knowledge of the unseen (which is only known through revelation) have almost no ability to actually state the Problem of Evil in a meaningful way.