The common thread that relates the first part of Psalm 19 to the second is glory and perfection. The psalmist seems to bask in God's word by speaking of His law, His precepts, His statutes, His ordinances, and His commands. Yes, I have felt that way. I have felt revived, that I am wiser than I should be with the limited formal education that I have, able to see more clearly, and joy to my heart when things seem to be falling apart around me. David's wonder in creation seems to affect him profoundly. he gives creation the ability to speak without words, just by its action. "The heavens declare...they pour forth speech....they display knowledge..." It is almost as if he is saying that the creation worships God.
In the classic prayer of verse 14, David is asking God to control the words of his mouth and the meditation of his heart. Personally, I have realized that I need to pray verses 12-13 just as much. I am certainly not aware of all of my hidden faults (but some of my friends are more than willing to point them out!) I need God's forgiveness for even my hidden faults. Willful sins. I would also have that they wouldn't rule over me. I'm grateful to my Savior, that as I'm ready to see them, he cleanses and enables. I like the promise David makes: "Then I will be blameless, innocent of great transgression."