Old Testament Law: Salvation by Acts?

We consider the common belief that Christ replaced a notion of justification by following the intricacies of Mosaic Law with justification by faith alone.  Is this true?  What did the Jews of Jesus' day truly believe about being made righteous in the eyes of God?  We talk about Jewish man I visited in the hospital and two rabbis who had come to see him.  The group of us talked about misconceptions that Christians have about the relevancy of Jewish beliefs and the Old Testament today.  We consider what it means for us, as Christians, to have been, as Paul put it, grafted onto the Jewish tree.