One of the godliest men who ever lived was also a man who comsigned a brave, noble warrior to death so that he could steal his wife (with whom he had already had an illicit relationship - II Samuel 11; Acts 13:22).
King David suffered terrible consequences for his depraved sin against Bathsheba and her husband Uriah, a shameful episode that Scripture chronicles in all its shame and gore. Nevertheless, the New Testament does not mention his waywardness, or anything at all in negative terms concerning David. He rather shines forth as "a man after Mine own heart," and most importantly, the New Testament writers frequently affirm the relationship between the Psalmist and the Lord Jesus Christ. "Remember that Jesus Christ of the seed of David was raised from the dead" (Acts 13:22; II Timothy 2:8).
Surely no overlooking or minimizing of sin is implied by the New Testament omission. Instead, the Holy Spirit would spotlight and maximize the wondrous grace of God, or as the Apostle Paul affirmed, "Where sin abounded, grace did much more abound" (Romans 5:20). The mercy of the Lord Jesus Christ provides forgiveness and cleansing to the humble, repentant heart far beyond any measure we can conceive. The Bible provides the most vivid description of such infinite span, declaring that "as far as the east is from the west, so far hath He removed our transgressions from us" (Psalm 103:12). That's a long way, a long way of grace, and a distance which we do well to establish and often nurture in our fundamental doctrines and beliefs.
The horrors of sin most reveal themselves when compared with the extent to which God went to provide forgiveness, and the extent to which we are forgiven when we avail ourselves of His mercy. The Lord Jesus Christ was tortured to death and forsaken by God and man in order to make possible forgiveness and newness of life. Those who believe are so justified that God "will not impute sin" to them (dealing with them as a loving Father rather than a condemning judge - Romans 4:8). David of the Old Testament trusted in such a coming redemption, and was so justified that the New Testament never mentions the very real wickedness of his sin with Bathsheba and Uriah.
Let us remember this when our spiritual enemies would claim that no hope of restoration exists for ourselves or others when we fall into deep pits of unbelief and disobedience. No greater lie has ever been told. Indeed, if we will come by the way of grace through faith paved by the Lord Jesus, and stained by His blood, we will discover with David a Father who runs to greet us with forgiveness and restoration. And, in perhaps the most redeeming aspect of His mercy, we will hear the voice of the Spirit in the pages of Scripture as He proclaims the one thing that a God of infinite understanding forgets...
"Their sins and their iniquities will I remember no more."