Openness theology is a sort of halfway house between traditional Christian theology and process theology. Much of the motivation for it rests in its theodicy, the attempt to reconcile the occurrence of evil with the existence of an omnibenevolent God.
According to process theology, God is dependent on the world; as such, he is unable to directly cause any events, but can only "woo" free agents (free in the libertarian sense) to submit to his will. This absolves God of evil fairly easily: God doesn't stop evil because he can't. Such a view, however, can't be reconciled with Christianity, or even theism -- it's panentheistic rather than theistic. God cannot perform miracles, such as the creation of the universe or raising Jesus from the dead. It exchanges God's omnipotence for impotence.
Traditional Christian theology has claimed that God, being omnibenevolent, is not responsible for evil. Human beings, being free agents, are responsible for most of the evil that they experience. God, however, allows such evil, but then uses it to bring about good. Jesus' crucifixion is the paradigm for this: the one innocent human being that has ever lived was brutally tortured and executed. Yet, by his death, the human race is reconciled to God. In fact, this seems to suggest that the greater the evil, the greater the good that God can bring out of it.
Openness theologians and philosophers object to this scenario, since it would mean that God foreknows horrific evils and doesn't stop them. God knew the Holocaust would happen, recognized it as evil, and then let it happen anyway. By allowing evil to take place, God is culpable for it, and this is incompatible with his omnibenevolence. They consider this to be simply unacceptable. God must not know that evil will take place before it happens, and therefore he must not know anything before it happens. The future is "open". It is not already laid down for us in the divine mind. We are free to choose the evil or the good. Of course, traditional Christian theology says we are free as well, but openness theologians do not think this view of freedom is acceptable, partially, again, because it makes God bear much of the responsibility for evil.
But this raises enormous problems for openness theologians, not least of which is whether their theodicy really accomplishes what they think it does. First, although God may not know infallibly what will happen, does that mean that he has no idea whatsoever what the future holds? To deny this would seem absurd: human beings can often know what's going to happen before it actually does, and while this knowledge is certainly fallible, it still allows us to sometimes see evil approaching before it reaches us. Thus, openness theology does not deny that God may know with great probability what we will freely choose to do, he just doesn't know it with absolute certainty. But this raises the question, how often is God right? Wouldn't it be possible for God to know everything with such a high degree of probability that he's never wrong? If so, we're faced with the same problem of evil as traditional Christianity has wrestled with; if not, why not? If God's foreknowledge is not infallible, on what basis does the openness advocate determine the degree to which God can know our future free decisions?
So the openness theologian's claims would seem to suffer from the same critiques which he gave to traditional Christian theology: if God knows that a particular evil will probably transpire, why wouldn't he stop it? The only way out of this for the openness theologian that I can see is if every instance of evil goes against what God expected would probably occur. But surely this is preposterous; after all, Nietschze predicted that the twentieth century would be the bloodiest that humanity had ever seen, a prediction that was fulfilled. Would the openness theologian maintain that an atheist philosopher had more insight than God? (If so, the atheist philosopher would appear to be right. Perhaps Nietschze meant to say God is dumb instead of dead.) The point here is that human beings have some capacity to successfully prognosticate when bad things will happen, so it would seem absurd to deny God the same faculty. The difference is that God supposedly has greater motive and ability to intercede.
Even if God were surprised by every instance of evil, this would still leave openness theology with a less adequate theodicy than traditional Christian theology. After all, according to the latter, God allows specific instances of evil only to prevent greater evils or to produce good. In the openness view, God is surprised by specific instances of evil, has no purpose in allowing them to continue, but allows them to anyway. Openness theology claims it is completely implausible that God could have had morally sufficient reasons for allowing the Holocaust; it's more reasonable to think that God didn't know the Holocaust was going to happen. But if this is the case, why didn't God stop it once it started? Why didn't God intervene and stop the Holocaust when it first began instead of letting six million Jews be killed over several years? The traditional Christian theologian can claim that God had morally sufficient reasons for allowing the Holocaust. The process theologian can claim that God was incapable of stopping it. But the openness theologian must maintain that God had the capacity to stop the Holocaust, had no morally sufficient reason not to, but didn't anyway. In other words, their attempt to build a better theodicy has produced the very worst theodicy possible, short of maltheism.