The question rests on a premis that is anti-thetical to Christianity. Namely, that Christianity is chiefly concerned with the actions of the individual, rather than his relationship with God. It is akin to asking whether all Germans must eat sauerkraut or if all French women must be thin. There may be a correlation, but there is nothing in the essence of nationality that demands a gastronomic course of action.
Yes, there is, amongst Christians who desire to grow in their relationship with God, a desire to avoid sin, but that is not the point. Christianity is focused on those actions which foster a deeper relationship with God. It is a focus on a personal progression towards perfection - not how to go about punish those who do wrong.
Indeed, and I mean no slight to Islam.SE or Judaism.SE, but just a few minutes look at those sites in comparison to this shows how completely different the focus is. Just about every question on Islam.SE and Judaism.SE can be boiled down to "What is the correct way to perform X." These are ortho-practic beliefs in the extreme. The point is the proper execution of a ritual. By contrast, Christianity is ortho-doxa. It is focused on a right understanding that is evidenced by ortho-practicum - right action. Right behavior (and by extension punishment for wrong behavior) is merely a secondary consequence of the right belief that the Christian faith commends.
A worked example: The Woman Caught In Adultery (John 8)
The story of the woman caught in adultery that you cite (John 8) is an example of this emphasis, and precisely why this question makes so little sense to a Christian expert. In the story, a woman is caught sinning. (Why the man isn't brought here, we don't know; presumably she was not commiting adultery in isolation. But, I digress.) The Pharisees, who understood the purpose of their faith in general and "the Law" in particular, purposely set up a situation to "catch" Jesus in His message.
Jesus' message was one of forgiveness - that any who desired to be forgiven could be.
At the same time, Jesus was not preaching a lax way of living. He had no room for people who would do away with the law. Indeed, as the Sermon on the Mount tells it, Jesus said anyone who just looks at a woman lustfully was guilty.
So, these Pharisees thought they had Jesus trapped. By finding a guilty woman, they hoped to force Jesus to equivocate. They expected he would either punish her or else look like he didn't care about morality. If the focus was on the action, then Jesus would have had to react to the behavior in some fashion.
Instead, Jesus turned the tables. He turned the focus back on love. He simply reminded those who would show no mercy that they themselves required mercy. The story says that Jesus simply started writing, and that each one of the Pharisees slipped away, from the oldest to the youngest.
In the end, Jesus says to the woman, "Where are your accusers?" He doesn't say, "Oh, keep on doing what you are doing!" Instead, he simply says, "Go and sin no more."
Punishment is not the point. Perfection is. Punishment is focused on a negative. Sin is the absence of a thing, and Jesus is about a presence. By completely fufilling the letter of the law, Jesus shows that punishment is not the point, but rather that mercy, forgiveness, and growth is.