My understanding is that the Christian bible states the Mosaic Law, but this law was superceded when Jesus arrived. But the Jews don't believe Jesus is the Messiah, so are still under the Mosaic Law? Is this the same thing?

That's true about the 'obvious' being stated in law. Like the disposal of excrement outside the camp - we know it as obvious today, but back then, they probably didn't appreciate the health benefits that we understand now with modern science etc.