From The Philosophy of Religion:

The first problem “the paradox of omniscience” is derived from Cantor’s proof that there is no set of all sets. Omniscience, it is said, entails knowledge of the set of all truths. Cantor’s proof, however, demonstrates that there is no such set. As there is no such set, it is argued, there can be no omniscient being.

The second problem is the problem of experiential knowledge. Here the argument is that there are certain facts knowledge of which can only be acquired through certain experiences—knowledge of what it is like to sin, for instance, can only be acquired by sinning—and that some of these experiences, and so some of these items of knowledge, are such that they cannot be had by God.

The third problem is that of reconciling freedom and foreknowledge, specifically the existence of divine foreknowledge with the existence of human freedom. If God knows all of our future actions, then the future is fixed, but if the future is fixed, it seems that there is nothing that we can do to change it. The ability to determine our future actions, though, is what constitutes human freedom. Divine foreknowledge, then, seems to preclude the possibility of our being free agents.

The fourth problem is the problem of middle knowledge. Middle knowledge is knowledge of what free agents would have done had the world been other than it is. As the agents are free, their choice of action cannot be determined by the state of the world, and so cannot be calculated on that basis. As middle knowledge concerns counterfactual situations, however, neither can their choice of actions be known by observation of the future. With the two possible sources of knowledge ruled out, it seems that middle knowledge is an impossibility.