One might define 'opinion' simply as "a belief or conclusion held with confidence but not substantiated by positive knowledge or proof". If that's accurate then, by definition, an omniscient being would have no opinions - for he would never fall short of knowledge.
But I'm not sure that this definition is correct. Patrick writes:
In many contexts, "opinion" seems to have definite connotations of weak justification or uncertainty; but I think, perhaps, they are just connotations... The fact that 'opinion', rather than 'knowledge' was used in the sentence will often be a reason to take it as meaning 'merely opinion' or 'opinion and not knowledge' even though the two aren't mutually exclusive.
Scalar implicature is the technical term for this semantic phenomenon. An underlying assumption of communication is that the speaker will convey sufficient information. If a set of statements can be compared in terms of their relative informational strength, we can assume the speaker chose the strongest possible statement. So we infer that any stronger statements are false (even though this isn't strictly entailed by the statement).
Consider: "Ten guests came to a dinner party. One guest died of food poisoning." Strictly speaking, all this entails is that at least one guest died, and possibly more. But of course we infer that only one guest died; for otherwise the speaker surely would have said more. Similarly, if I say something is "possible", you will usually infer that it is "not certain" - even though that's not a strict entailment.
Now, it may be that <opinion, knowledge> is a scalar ordering much like <possible, certain>. This could explain why we find it odd to call knowledge 'opinion'. Knowledge is the stronger term, so we should attribute that instead whenever both are true. 'Opinion' alone would implicate 'not knowledge'.
But how can we tell whether the strangeness we observe is due to contrary implicature or outright contradiction? The standard test is that implicatures can be 'cancelled' by further clarification. I could say "one guest died - indeed, several did", and this is not a contradiction. We no longer infer that only one guest died. (Compare: "exactly one guest died - indeed, several did".)
So, how about this: "I am of the opinion that X is true; indeed, I know it is." That sounds like a reasonable statement, not a contradiction. This shows that knowledge and opinion are not mutually exclusive after all. Any appearance to the contrary is merely due to the connotations that arise from scalar implicature.
Alternatively, consider moral judgment. It seems natural to call value judgments 'opinions'. I think this holds even if we are realists and believe that there are objective moral facts. Being omniscient, God would know these facts, e.g. that murder is wrong. But I think it's still natural to concede that God has the opinion that murder is wrong. (Perhaps my intuitions are unusual here; as always, I'm curious to hear what others think.) So, at least in the case of morality, we can have opinions even about things we know. [I assume this case applies just as well to mortal people. If you doubt we can have moral knowledge, just replace 'we' with 'He'.]
We've established what opinion is not. But what is it, then? I think the key is not uncertainty, but subjectivity. By that I mean subjectivity of representation, not of truth. You can have opinions about objective facts, but the opinion itself is a subjective thing. There is a sort of 'agent-centeredness' to it. (I think that's why opinions and values go together so naturally - even for God.) An opinion is a relation between a person and a proposition, whereby the former entertains some sort of commitment to the latter. It's as if you were to say, "Well, based on my experience of the world, it sure does seem to me as if X is the case."
I think Patrick was getting at something similar when he wrote:
In order for god to have any sense of self at all (or any personality), he must have opinions. Sure, his subjective truth will correspond perfectly with objective reality, but thats what it means to be omniscient. Without an opinion, he wouldn't be god, he would just be objective truth.
What's interesting about this is that the introduction of intentionality almost threatens God's perfection. An essential characteristic of believers is that though they can represent the world, they can also misrepresent it. So if God can have beliefs, then he can have false beliefs. It just so happens that he doesn't, assuming he's omniscient; but such errors are within his powers (and 'nature') as an opinionated self.
Further, opinions and beliefs represent some proposition as true. It may even be true. But beliefs and opinions are not the truth, itself, directly; they're a step away, representing reality rather than embodying it. We may decide that the most perfect being would not be separate from truth. That is, rather than representing the truth, we may prefer to say that God is the truth. But then we cannot use personal pronouns, for there is no person left. Some impersonal 'truth' is not what most people are talking about when the use the word 'God'. So I think we should conclude that God can - indeed, must - have opinions.