June Thomas, writing in Slate, recommends Rev:

Rev.—about a lovable, bumbling Church of England vicar struggling to help his inner-city London congregation, please his superiors in the church, and serve God—is both too gentle and too swear-y for American television. The Rev. Adam Smallbone, played by Tom Hollander, is the ultimate straight man: He displays extraordinary patience when dealing with heckling construction workers, bullying archdeacons, undermining assistants, and challenging worshippers, but he always seems to find a way to stand up for himself and do the right thing. Rev. is both a rare TV presentation of a sincere man of faith, and a fabulous example of a sly, understated brand of British humor. 

Now I suppose as an Anglican clergyman myself (working in a downtown urban parish) I'm the target audience for the show. My very non-church going wife and I love watching this show together. Rev wonderfully depics the marriage of Rev. Adam and Alex Smallbone (she's a lawyer). Alex is a very non-traditional clergy wife--including glimpses of her kinky side (warning: somewhat NSFW).

The show touches into some areas also not commonly depicted in clergy tv shows. In the second season, the drug dealers who sling behind the church leave crack in the garbage cans for easy access. Unfortunately squirrels start getting into it and start jonesing creating havoc for walker bys. One poor squirrel even overdoses. 

At the same time there is a very touching side to the show as June Thomas mentions. There are great meditations on sin, ethical ambiguity, the (largely hidden) inner pain of urban life. 

Below is one my favorite scenes, from the first season. The good Reverend loans out the church to a burgeoning mega-church star-pastor with a growing young congregation. Adam's own flock is small and struggling and the lure of this infusion of youth and energy is hard to resist. But the episode deftly portrays the problems attendant with such superstar forms of church life. It also touches into a particuarly difficult area of church ministry--i.e. sexual ethics with a span of ages and in particular amongst broken, often lonely people. The brilliance of naming the Christian rapper Ikon (Icon) and what that says about idolatry in our civilization--especially in churches--is worthy of special consideration. I must also confess that I would very much like to pour liquor in the smoothies I drink in church (my typical Sunday morning breakfast). 

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Update I: One of the other great characters in the show is The Archdeacon, Adam's boss.