Amen, Aelfwine; righteousness we can never gain thorugh the law. Now to be sure, we must keep the law for it is good, but we can never obey to necessary level for us to be as righteous as God requires in order for us to go to heaven.
One other error that is most commonly believed is that while many others acknowledge that we cannot be righteous enough, that is to be obedient enough to the law to be saved, the same believes that we can cooperate with God in obtaining salvation. They're not denying the impossibility of, but at the same time, think that if we do our part... then He'll do His part.
1st of all, if the scriptures say that no one shall be justified by the law, then why would God go back on His word? It's like saying, "Yes, we cannot hope to break the law of gravity, but if you jump high enough, and flap your arms, the air will do it's part"
2nd, there is no scripture to back that notion.
Whenever you see someone adding a "But" after acknowledging an irrefutable truth, you will most likely hear a false teaching.