What could be a problematic effect of granting States to much power to pass their own laws?

Laws would vary from one State to the other, which would make it difficult to adhere to if you're not from that State. Also, politics would play into effect. I'd like to use the American Civil War as an example; some states were for Slavery, meanwhile others sided on the abolishment side. That could come into play here, and that could be extremely dangerous.