How is it that an unchanging and omniscient God can have "regret" as He did in Gen 6:7?

Keep in mind that God allowed humans the privilege of free will, knowing the consequences, because he trusted man.

In an earlier verse, Genesis 6:5, the reason for God's regret is described:

The Lord saw that the wickedness of man was great in the earth, and that every contention of the thoughts of his heart was only evil continually.

In this case, the consequence of God's granting man free will was that man grew wicked.

Don't think of it as a mistake--think of it as though God regretted creating man the way he did.

Is God completely unchanging in God's dealing with humankind? The scriptural evidence about incidents of prophetic intercession suggests this is not always the case.

For just one example to the contrary, consider a couple of divine-prophetic dialogs. One is the dialog with Abraham, where Abraham held out for mercy against the people of Sodom. http://bible.oremus.org/?ql=147474699%20 (NRSV). In this example Abraham prevailed in the dialog but the outcome did not change.

For another example, here Moses recounts his dialog. (NRSV, Deut 9:11-21)

At the end of forty days and forty nights the LORD gave me the two stone tablets, the tablets of the covenant. Then the LORD said to me, "Get up, go down quickly from here, for your people whom you have brought from Egypt have acted corruptly. They have been quick to turn from the way that I commanded them; they have cast an image for themselves."

Furthermore the LORD said to me, "I have seen that this people is indeed a stubborn people. Let me alone that I may destroy them and blot out their name from under heaven; and I will make of you a nation mightier and more numerous than they."

So I turned and went down from the mountain, while the mountain was ablaze; the two tablets of the covenant were in my two hands. Then I saw that you had indeed sinned against the LORD your God, by casting for yourselves an image of a calf; you had been quick to turn from the way that the LORD had commanded you. So I took hold of the two tablets and flung them from my two hands, smashing them before your eyes.

Then I lay prostrate before the LORD as before, forty days and forty nights; I neither ate bread nor drank water, because of all the sin you had committed, provoking the LORD by doing what was evil in his sight. For I was afraid that the anger that the LORD bore against you was so fierce that he would destroy you. But the LORD listened to me that time also.

The LORD was so angry with Aaron that he was ready to destroy him, but I interceded also on behalf of Aaron at that same time. Then I took the sinful thing you had made, the calf, and burned it with fire and crushed it, grinding it thoroughly, until it was reduced to dust; and I threw the dust of it into the stream that runs down the mountain.

So here is recounted a change of the divine mind in response to prophetic intercession.

It has to be said, "don't try this at home, kids." Moses was willing to place his own favor with God on the line to get God to relent against the Hebrew people.

My point: every time I think I've studied enough to make simple statements about the mind of God, something surprises me and brings me up short.

God is completely unlike us, so any attempts to describe God using human language are very limited. In this case an attempt is made to express the sorrow of God over the evil and pain introduced into the world, even though he knew it would happen, and he knows he will not only put it right, but make things even better than they were. This passage shows that God is not indifferent toward our problems.