You are confusing God's law with mosaic law. God's law is the 10 commandments, everything beyond that was added by man.
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You can't have it both ways. If the bible is supposed to be the word of God then why would the word of God (as he has told it to the authors) be wrong?
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It's not wrong. It tells very plainly that Moses was judging all of the cases in Israel, which he then appointed judges. In order for them to do so effectively, they wrote details of the law God gave. They then added to it so that future generations would have precedent for cases much like any other legal system does. Jesus points this out when he says divorce was never supposed to be allowed, but Moses allowed it due to the hardness of men's hearts.