Interesting thought Vern. When He says of our sins that He will "remember them no more" does He really forget them? I certainly remember them and He knows my thoughts and my words.
I certainly hope so! What that means? Hebrew 8:12 and 10:17 both refer to God not remembering sins. Perhaps someone who is more familiar with the Greek than myself will respond, but as I understand it, the word "remember" is mnaomai and means to bear in mind, to recollect, and with the idea of reward or punishment. In the sense they are forgiven, this aspect of knowledge is covered by God's mercy and grace, and are no longer held against us.
I think that though God has all knowledge, he chooses not to bring those things to remembrance. For us, the hardest thing in the world is to forgive ourselves, or so it seems to me.
My understanding is that forgiven sins are "off the books", as in no longer imputed to us. God does not take them into account when judging us, because the penalty for our sins (those who are Christians) is marked "paid in full". He forgets them with regard to us, but He still could call them to mind, He just doesn't where Christians are concerned.