This story is intriguing on several levels.
First, Herod had James killed, but had Peter arrested. Could that have been because of his high profile and popularity? Could they have feared his spiritual power and authority? Was it because the Church was praying for him? Maybe all of the above.
Second, I can't help but notice the difference between a man motivated by political popularity (Herod) and one who operated by principle (Peter). As a result, Herod lived in fear as a people-pleaser while Peter lived by faith, pleasing God. Herod might have been in control but Peter was in charge!
Third, Herod surrounded Peter with guards. God surrounded Peter with angels. That was true because of two reasons: Peter was in God's will and the Church mobilized in prayer.
Fourth, angels are better than guards. When they woke Peter in the middle of the night, they slipped him out of the chains and out of the prison. The guards never knew the difference. When God wants to deliver His people - no chains or prison can hold them. People of faith are free even when they are captives!
Five, prayer is powerful! More powerful than they expected, apparently, because when Peter showed up at the site of their prayer meeting they were in disbelief. Has that ever happened to you? Have you ever prayed intensely for something and then found yourself surprised when God gave you what you asked for in a timely fashion? They went from belief to disbelief - then to greater belief!
There is tons of good preaching material here, but the bottom line is this, God will use anyone to overcome anything to accomplish the thing He wants accomplished. It doesn't take perfect faith, it just requires a perfect heart!
Pray persistently. Perservere consistently. Perfect your heart continually!