Traditionally we will talk about 3 uses of the Law.
1 - The Curb - the threat of punishment keeps general wickedness contained by fear of punishment.
2 - The Mirror - the Law shows and makes plain one's sin, so one know of one's need for a Savior.
3 - The Rule (or Trellis) - In a Christian, the Law provided direction for the new man.
A lot of times as Christians we key in on the second or third use. We think of the 2nd rule as the theological use - this is the typical use of a sermon where our sin becomes clear. Or we will focus on the third use - the instructive use of the Law - this is how we "ought to be."
I think we forget that as regards our lives here on earth, in time, that first use, the Curb, still holds a major impact. Part of the reason for this is that Christ and Grace doesn't mean that temporal punishments are done away with. If I knock off a bank, I'll still end up in the pokey even should I repent.
However, what about the simple, petty things that we do every day - the non-spectacular sins. If I am curt towards my wife, that might upset her. If I glare at a person who annoys me, that might come back to bite me. There are social and political consequences that result from our actions - and simply put, "You ought to forgive me" is true, but show me the person in this life who forgives perfectly.
We are told in Scripture that perfect love casts out fear, for fear deals with punishment. Yes, it is true that we will not receive punishment from God, for Christ has paid for all. Yes, is it true that we ourselves should be quick to forgive and forego punishment for those who wrong us (indeed, strive, strive for this!). But this is also true - we remain sinners in a sinful world - and our sin, even the small and unthinking ones have real consequences.
We would do well, once in a while, to remember the practical and tangible effects and consequences of our sin. Bruises are real, be they physical or emotional, and the bruised often swing back. This is good for neither. This is why Scripture can rightly warn even believers of this truth (think on Proverbs, if you will).
What it remains is this. I think the simplest approach is as this - A Christian is to strive to neither GIVE offense nor TAKE offense. Provoke not your neighbor to wrath, and be not wrathful yourself.
It's hard to do, but in this life, this is the struggle we must fight against sin.