Visible crew/equipment: When Jack opens the medicine cabinet to get the shaving cream, in the mirror's reflection you can see the camera as well as where the set ends.
Double Date - S3-E1
Visible crew/equipment: At the start, while Mr. Roper is in the kitchen the faucet sprays water and the doorbell rings. Note the cabinets and wall behind him. When Roper walks out of the kitchen, as the swing door is open we can see the kitchen, and the upper cabinets are split apart with the wall missing, so the area behind the kitchen set is visible. (00:00:50)
Visible crew/equipment: When Mr. Roper gets the idea that it's Jack's diary, Jack tells him not to worry and it'll be their own little secret, then in the next wide shot we can see the bank of set lighting at the bottom of the screen. (00:21:15)
An Anniversary Surprise - S3-E20
Visible crew/equipment: At the end of the episode when Jack falls back off the chair, a boom mic is very visible above him. (00:25:15)
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