I think so.

First, if God can't make mistakes, then there would be something he couldn't do. Yet God can do anything. Thus God can make mistakes.

One might object that though the person of God can make mistakes, he would cease to be God were he ever to make one (just as, by analogy, a bachelor can acquire a wife, but he ceases to be a bachelor when or if he does so). So, the person of God can make mistakes, but not 'as God'. (All one is admitting here is that God has the ability to cease to be God).

But I don't think that's true either. That is, I think God - as God - can make mistakes.

First, to make a mistake, it seems to me, requires a false belief. So can God have a false belief? Yes, why not?

Well, one might think that God cannot have a false belief for God is all knowing. However, as I have pointed out in another thread, to be all knowing is to be in possession of all knowledge. And knowledge involves having a justified 'true' belief. So, God could be in possession of all justified true beliefs, and also have some false beliefs as well. For an analogy: let's say I own all the world's Rembrandts. Well, does that mean I own no fake Rembrandts? No, for the claim that I own all the world's Rembrandts is entirely consistent with me also owning some fake Rembrandts.

Nevertheless, one might object that to be all knowing is to know all true propositions.

But that is false, for a) knowledge is made not just of true beliefs, but of justified true beliefs. So knowledge has at least two ingredients, not one. And thus being in possession of all knowledge is not equivalent to knowing all true propositions. It is to be in possession of all 'justified' true propositions. And b) there are clearly true propositions that it seems impossible to know. For example, take the proposition "It is raining, but no one believes it is raining". That proposition is capable of being true. Yet to believe it is to falsify it; and as knowledge cannot involve a false belief, that proposition - if or when it is true - cannot be known.

Thus, being all knowing does not involve knowing all true propositions. It involves knowing all 'justified' true propositions. At this point, then, it seems consistent with being all knowing that one has some false beliefs in addition to all the justified true ones.

However, one might object that God would nevertheless have to know that those false beliefs of his were false - for otherwise there would be something he did not know. But again, that's false and fails to take the above lesson. If God has a false belief P, then although the proposition "God's belief that P is false" is true, that is not sufficient to qualify it as an item of knowledge. Again, for a proposition to qualify as an item of knowledge, it has to be 'justified'. It is not sufficient that it be true.

What is a justification made of? Well, a justification is made of God's attitudes. That is, to be 'justified' in believing something is for God to favour you believing it. If that's true, then if God believes P, then God favours himself believing it, else he wouldn't believe it. And similarly, God disfavours himself believing not-P. And thus the proposition "God's belief that P is false" is one that God does not favour himself - or anyone else - believing. It is true. But it is not justified. And thus God, in not believing it, does not manifest a deficiency in knowledge.

Thus, I can see no compelling reason to think that God cannot make mistakes. God is omnipotent, omniscient and omnibenevolent. But possession of those qualities seems - at this point in my reflections anyway - to be consistent with making mistakes.