I had this idea.  One I fleshed it out, I figured I might as well share.
PC's have a big job.  They must accuse, judge and then punish NPC's.

If your town isn't "grabby" enough, and want to make the PC's job just a bit more difficult consider adding in Conflicting Punishment Goals between NPCs throughout the town.

Various goals of punishment follow, but they do not need to be mutually exclusive

Br. Gibbs attacks Br. Morris in an act of sinful malice and hate.  Morris suffers a ghastly knife wound and ends up losing his right hand.

Prevention- punishment should stop the specific individual from doing it again by making the punishment so bad the criminal will not want to do it again.

Sis. Allen feels that killing Gibbs' favorite horse, and if he does it again, the town will kill his favorite dog, is adequate punishment-- because she knows Gibbs loves his Collie more than life, and won't act out again if it would mean losing his pet.  She adamantly believes any other punishment is just cruel and pointless. 

Restraint- Punishment should focus on protecting society.  Isolate the criminal, or kill him-- just make sure that they don't have a chance to do it again.

Br. Moreland suggests exile.  Gibbs should be turned out of the town for two years.  Give him a chance to mature, learn to control his anger outside of the town.  If Gibbs is left in the town Moreland just won't feel safe.  

Rehabilitation- Treat the criminal, reform them, they don't need to suffer really-- just make sure they learn not to do it again.

Steward Dixon and Gibbs' father knows that if Gibbs just spends the next year as Stewart  assistant, studying the book of life, doing acts of service to the town that Gibbs will learn the compassion of the King of Life and will learn not to be violent.  Gibbs' father may really believe this is the case, he may even escalate to violence if the Dogs decide otherwise...

Deterrence- Make a public showing of the punishment and those who watch will be scared into acting correctly.

Br. Price advocates public lashings.  He may even take it upon himself to do the lashing, just to make sure people know how wrong Gibbs was...

Education- Use punishment as a tool to teach the public what is right and wrong.

Sis. Morris feels Gibbs should be publicly reprimanded each Sunday at church in front of everyone for the next month. He can't be exiled, and it would be just wrong if he was actually made the steward's assistant!!

Retribution- Restore order and give emotional closure to the victims by getting revenge.

Morris' father feels that just as his son lost a hand, Gibbs should have his right hand cut off, and given the chance he'll do it himself!

I'd only do this if the Dogs were dithering about what to do with their miscreants... which I've never seen happen.

I think it might backfire.  Part of the coolness of Dogs is that you never know how the Dogs are going to come down -- will they side with the underdog or the Steward?  The husband or the wife?  If you try to push the players by having Brother Kelley the Steward demand that they whip some guy or cut his hand off -- that's liable to push them in the other direction and and make the game less interesting. 

It would be interesting to give the players a table of possible punishments and see how they react to it -- maybe you could link it to the Ceremonies, thusly:
The Stocks: 1d4
Flogging: 1d6
Branding: 1d8
Maiming: 1d10

This doesn't fit the standard Dogs background so terribly well, but it would work well for a pseudo-Puritan or pseudo-medieval setting for Dogs, where they'd be expected to carry out draconian punishments. 

I like it, simply to add concreteness to what the NPCs want. I'd never worry about driving the PCs toward or away from anything; if they respond to what the NPCs want by always doing the opposite, that's their affair.

Everyone in the town agrees that Bro Gibbs needs to get it and hard, but which version of "get it and hard" do the Dogs go with? Whichever they choose, they've offended at least one person's very sense of the Justice of God - now how do they make it right with her?

Not bad.

-Vincent