Revealing mistake: Any time a main house light or a lamp is switched off, it is still bright from the studio lights.
Continuity mistake: In the very first episode, there is a silver light fixture hanging from the ceiling in front of the kitchen. The light fixture appears and disappears throughout the first season.
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