Although God is omnipotent, He really CANNOT do the following things because they are against His very nature.
God's very essence includes complete truth. It is one of His attributes. In Him we will never find any deceit. Accordingly, we can completely trust God, His Word, and His promises.
“That by two immutable things, in which it was impossible for God to lie, we might have a strong consolation, who have fled for refuge to lay hold upon the hope set before us:” (Hebrews 6:18 KJV)
“He is the Rock, his work is perfect: for all his ways are judgment: a God of truth and without iniquity, just and right is he.” (Deuteronomy 32:4 KJV)
“Into thine hand I commit my spirit: thou hast redeemed me, O LORD God of truth.” (Psalms 31:5 KJV)
God is All-Knowing...so therefore nothing you do surprises Him—i.e., you really cannot “disappoint” God as we humans use the term, because He already knew you were going to do it before the foundations of the world. Of course, this doesn't mean that our actions cannot “hurt” God, and in fact, our sins created the need for Jesus to die on the cross. However, God knew this and sent Jesus to die to reconcile us to Him. So believers in the Lord Jesus Christ can always turn to God for forgiveness.
“If we confess our sins, he is faithful and just to forgive us [our] sins, and to cleanse us from all unrighteousness.” (1 John 1:9 KJV)
“For if our heart condemn us, God is greater than our heart, and knoweth all things.” (1 John 3:20 KJV)
“Great is our Lord, and of great power: his understanding is infinite.” (Psalms 147:5 KJV)
“Declaring the end from the beginning, and from ancient times the things that are not yet done, saying, My counsel shall stand, and I will do all my pleasure:” (Isaiah 46:10 KJV)
While God is all-knowing, He chooses not to remember sins that are forgiven. We as humans have a difficult time doing this. It is not a matter of knowledge, but a matter of choice. On a limited basis when I choose to forgive someone, I have the ability to not remember it. When it begins to enter my mind, I choose to put it out of my mind. God, who is infinitely more powerful, has the ability to always choose to not remember our forgiven sin. We know this because His revealed word tells us.
“And they shall teach no more every man his neighbour, and every man his brother, saying, Know the LORD: for they shall all know me, from the least of them unto the greatest of them, saith the LORD: for I will forgive their iniquity, and I will remember their sin no more.” (Jer 31:34 KJV)
“As far as the east is from the west, so far hath he removed our transgressions from us.” (Psalms 103:12 KJV)
“Now then we are ambassadors for Christ, as though God did beseech you by us: we pray you in Christ's stead, be ye reconciled to God. For he hath made him to be sin for us, who knew no sin; that we might be made the righteousness of God in him.” (2 Corinthians 5:20-21 KJV)
Another attribute of God, is that He is light. Pure light eminates from God. In fact, in the future heavenly city, there will be no need for the sun or moon, for the very light that eminates from God will provide all the light we can ever need.
“This then is the message which we have heard of him, and declare unto you, that God is light, and in him is no darkness at all.” (1 John 1:5 KJV)
“And the city had no need of the sun, neither of the moon, to shine in it: for the glory of God did lighten it, and the Lamb [is] the light thereof.” Rev 21:23 KJV)
“And there shall be no night there; and they need no candle, neither light of the sun; for the Lord God giveth them light: and they shall reign for ever and ever.” Rev 22:5 KJV)