David Wilkerson emphasizes that it is possible to walk before the Lord with a perfect heart, as commanded by God to Abraham and echoed by Jesus in the New Testament. He clarifies that perfection does not equate to being sinless, but rather signifies completeness, maturity, and a responsive heart that is obedient to God's voice. Wilkerson highlights the importance of allowing the Holy Spirit to reveal hidden sins and the necessity of a heart that desires to be cleansed and made pure. The perfect heart is characterized by a willingness to listen and respond to God's guidance, ultimately leading to a deeper fellowship with Him.