Here is a really useful little paper by Theodore M. Drange on the contradictory aspects of God. Drange is Professor of Philosophy at West Virginia University. This article can be found here, at Philo online. This gives a neat little summary of many of the arguments against God based on his characteristics being incompatible with each other. The classic one, as touted by Dan Barker (and myself, often) is that God cannot be perfectly merciful and perfectly just at the same time. See what you think.