Verse 5 – At the beginning of each month, the Israelites gathered to celebrate the New Moon festival. Other nations worshiped the moon itself. The Israelites, however, celebrated the festival at the time of the new moon, when the moon was not visible in the sky. Nothing in the creation is to be worshiped only the creator.
Verse 15 – Jonathan asked David to keep a promise to treat his children kindly in the future. Years later David took great pains to fulfill this promise (2 Samuel 9).
Verses 31, 32 – Saul was still trying to secure his throne for future generations even though he had already been told his dynasty would end with him (13:13, 14). Jonathan could have made a move to become the next king by killing his rival, but he bypassed this opportunity because of his love for both God and David (23:16-18).