Jesus lived in perfect obedience to the law, and he practiced what he preached and preached what he practiced, so everything he taught was in accordance with the law. In John 6:38, Jesus said he came only to do the Father's will, and in John 7:16, he said that his teachings were not his own, but that of the Father who sent him, so Jesus did not go off on his own and teach something other than what the Father had commanded. God's law is perfect and eternal (Psalms 19:7, Psalms 119:160), so there is no better law, and Jesus did not give a brand new one.
The command to love one another is found in Leviticus 19:18, so there is nothing brand new about that command. Jesus loved us through his obedience to the law, so if we love one another as he loved us, then we will also live in obedience to it. There are two Greek words that are often translated as "new", with "neon" meaning "brand new with respect to time" and kainous meaning "refreshed or restored with respect to quality", and the word used in John 13:34 means new with respect to quality. In other words, there was nothing brand new about the command to love one another, but what was new was the quality of the example with which we are to obey the command. Another place where we can see this distinction is in Matthew 9:17, where two different words are often translated as "new", but it means brand new wine being poured into restored wineskins.
http://biblehub.com/text/john/13-34.htm
Jesus summarized the law as being about how to love God and how to love our neighbor (Matthew 22:36-40), so a person who loves God and our neighbor will not disobey any of the commands in the law.
The context shows that James was encouraging them to be more consistent in their observance of the law, not saying that they shouldn't bother trying to keep it. The consequence of breaking any part of the law is not that we won't be justified because we aren't to keep the law in order to become justified in the first place, but rather the consequence is sin, which means that we need to repent and turn back to obedience to the law. James was not saying that breaking the law causes us to be guilty of breaking other laws that we did not break, but that breaking any of the laws has the same consequence of sin. There is indeed no condemnation for those who are in Messiah (Romans 8:1), but those who are in Messiah are those who ought to follow his commands and walk in the same way that he walked (1 John 2:3-6), which is in obedience to the law.
