A couple lines from The Departed I don't get

I rewatched The Departed for the 1000th time today and there's a couple lines I still don't get. One is where Alec Baldwin says someone is "straight outta Going My Way." And the other is when Jack Nicholson is mad at the guy about the body being found and he says "Don't laugh, this isn't reality TV!" What...?

I don't remember specifically but I'd guess he's talking about someone seeming like they'd be a character from the movie Going My Way. Maybe a priest? Not sure the other.

Could be I guess. Wahlberg mentioned a pedophile priest in a scene before that, maybe it's the same character