Jack Bares All (a.k.a. Oh, Nurse) (2) - S6-E2
Continuity mistake: In the scene where Terry puts on the gag glasses, notice how the black circles under her eyes get larger after the shot changes.
Gigolo Jack or Professor Jack - S6-E4
Continuity mistake: In the scene where Terri admits to Jack that she mistook his cooking lessons for lovemaking lessons, look at Terri's bangs. They go from on her forehead to brushed back then back to on her forehead then back to being brushed back.
Continuity mistake: In the scene where Jack, Janet and Terri are on the air for the cooking show, Janet holds up the silver bowl but there is no parsley in it. Then in the next shot the bowl is instantly full of parsley.
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