This man after God's own heart who had fought lion and bear by faith, brought down Goliath, refused to hurt the Lord's anointed, and taught Israel about God through many psalms fell into adultery and murder one day. The whole nation must have known about it, but he seems to have been blind to it till the prophet Nathan confronted him. These two parts of David's life do not seem to match. Though the Bible does not say how this happened, we can perhaps make a guess in order to learn some lessons for ourselves.
Perhaps David thought that since he was the king who made rules for the nation, he was not accountable to the people. But then he forgot that he was indeed accountable to God. Perhaps he thought that no one knew about it except Joab his commander and so he could get away with it. But perhaps no one dared to talk to him because he was the king and their own life would be in danger if they questioned him!
If we are in a position of authority over some others perhaps the reason no one points out our sins may be just that. Perhaps people are just too polite about it or thinking that it is none of their business. But does it mean that we are without sin if no one is talking about it? We are accountable to God who is everywhere, in whose eyes there is nothing hidden and who knows even the thoughts and intentions of our heart (He.4:12,13). Our standard of measuring our spiritual progress is not what people think about us or how much we are 'serving God' but what goes on inside us -- what we think about ourselves in the secret of our thoughts, what we do away from the eyes of man, why we do what we do, how honest we are before God about every detail of our life, etc.
There is nothing much great if we acknowledge our sins when we are caught. But our honesty before God is tested by how we deal with God about the details of our private lives on which we are not even likely to be caught by people! Here again, why we speak and do things is more important than our deeds themselves. If we really want to become spiritual, we have to learn to live before God (Ge.17:1;Jas.4:10), irrespective of the good or bad opinion people have about us. It is also likely that if we have a reputation built on our gifts or ministry, people may have a better opinion about us than is true! But, in the ultimate analysis, the only thing that will count is what God thinks about us, and there is no fooling Him.
When Paul's turn comes to receive a crown from the hands of Jesus who will tell him, "Well done, you good and faithful servant," Paul may give the Lord the crown back reminding Him that He deserves it for showing grace to a blasphemer and persecutor (Re.4:10,11). It is that kind of humility and honesty that will earn him a crown first of all! In spite of all the name and fame Paul received among Christians, he was also honest enough to see that there was nothing good in his flesh (Ro.7:18) and that he was still doing things he didn't want to do (v.20).