The notion of a priest-detective seems inherently paradoxical: forgiving sin vs. seeking out the guilty, mercy vs. justice, the confessional vs. the interrogation. But G.H. Chesterton was fond of paradox, and in these stories he's generally successful in presenting a character whose pastoral experience combines with his detective instincts to ensure that TRUE justice is done.
I first read the stories as a Catholic high school student, when I accepted the author's religious assumptions without question. But when I read the book again as a formerly Catholic adult, I was pleasantly surprised: Father Brown is (usually) unsanctimonious and free of legalisms regarding sin. Furthermore, he distinguishes between someone whose sin arises out of a fundamentally generous spirit (like Flambeau), vs. those who sin from coldly selfish motives based on greed or arrogance.
Chesterton is a memorable writer, if prone to excesses of purple prose; but when he's at his best, nobody comes within a mile of him. And, while his plots can be far-fetched, he works them out with great ingenuity and thoroughness. Some of the stories should be read with tongue firmly affixed in cheek, but they're fun, memorable, and thought-provoking.