Continuity mistake: While Jack is talking to the police officer about the missing rent money, they are standing in front of the TV set and the front door is open. When it cuts back to Jack and the officer, over Jack's shoulder the front door is closed, but when the officer turns to leave the door is open again.
Revealing mistake: When Jack and Janet are in the entry looking around for burglars, their voices are over-amplified, indicating they are in a sound studio.
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