The basic question has to do with how our lives are defined by faith in Jesus in ways that are different than the lives of the Jews were defined by their commitment to the law. It touched on how we define "faith" and "law". Faith must be more than mere recognition of the existence of Jesus, reaching to the place where we respond to Him as King and Lord, and as such removing ourselves from the position of authority, preference, control. Law references more than a basic set of instructions on how to live (that can now be ignored because Jesus changed all that...not quite), and encompasses the entire OT system that defined how someone HAD to behave in order to remain in good standing with God. We talked about how the new relationship given by grace through Jesus no longer relies on these rules and details for living, but we are still responsible for deferring to Jesus as our Savior, which has definite effects on how we live.
But surely the opposite extreme is wrong...that Jesus has saved us, therefore we can do whatever we want because ultimately it doesn't matter. We know in our bones that this is lacking as well, because the power of Jesus' death shouldn't serve to let us off the hook but to hook us into His kingdom in a way we are incapable of achieving alone.
It was a big enough deal and a difficult enough question to put Paul and Peter in face-to-face opposition. Knowing that neither of these guys was all that laid-back and subtle, it must have been a serious discussion. We only see Paul's side, but the point we can glean from the encounter is that this really matters, and isn't easy to nail down.
For an initial, simple consideration, I think it comes down to the order of things. Originally, the Jews believed that this life described in detail by God was the means to their continued relationship with Him. I believe the intention behind God providing this list of do's and don'ts included a desire for them to live well, be healthy, remember what mattered. It wasn't just to whip them into submission to His will, though He does want that. He wanted them to know what a good life should look like.
Jesus repeated the same. He reiterated the old laws, with new understandings. Don't just draw the line at murder; back waaaaay up from there and don't even concern yourself enough about your preferences to be offended by the actions of another so that you don't even become angry. Don't just love those who love you, but choose to seek good (love) for those who refuse to do the same for you. These are the kinds of attitudes, thoughts and behaviors that can actually transform a person from being selfish, petty, and demanding to being sacrificial, kind and loving. But He took it even further. Instead of saying, "Do these things in order to have a good life.", He said, "Here is my good life and you can have it. Now use it the way I showed you."
The right living follows the right relationship with God, rather than requiring right living in order to reach and maintain the right relationship with God. Thus, the holy, healthy life that we want to live today may not really be all that different from the way the Jews lived (specific details of their interpretation aside). We still shouldn't murder, covet, lie, steal, work without rest, etc. But we absolutely cannot imbue those actions with saving power.
We must remember that Jesus has completed all redemptive action. Done. Period. He granted us the gift of the opportunity to pursue a life that pleases Him with no strings attached. However, if we really grasp who He is and what He has given us, we should be unable to honestly say that the way we live has no bearing. Not because it can or cannot save us, but more because it shows whether we understand who it is we are following. If we are not living with intent to please Him, we must not quite get Him.