Factual error: Jack takes Cheryl's phone off the hook and puts it down, but while the two are talking throughout the two-minute scene, the phone does not make the loud annoying buzzes that occur after 30 seconds or so from the phone being off the hook (which happened back in the years the show aired).
Character mistake: Jack hands his pants off to Terrie at the opening to fix a tear, acting like he's never done it before when he was a cook in the Navy and should know how to do that himself as a very basic skill.
Answer: He's not a Catholic priest. He's a pastor, with the title Reverend, at a community church who chooses to wear a clerical collar. Some people still address pastors as "Father" though. I'm not sure of his religious denomination, but most pastors can marry.
Bishop73