Why is Peter needed to bring Cornelius into a relationship with Christ (consider: Matthew 16:18-19; Acts 8:14; Acts 15:6-11; Galatians 2:11ff)?
How does God use leaders in the kingdom today? What might be a parallel example between this situation and one the church might face today?
Is there a significance to the vision repeating three times (consider: Luke 22:34 & John 21:15-17)? What's your number (how many times does it take God to get your attention)?