Do they have a law in SD saying you have so many days to update your address after moving? Could be a problem if so.
I would think you would want to have all your I.D.'s reflecting the same and correct address.
I could see problems if you get stopped and the officer says, "SD permit but Utah drivers license. Something ain't right."
Course, I don't know what the law is in SD. In Florida, they want you to submit a change of address within 30 days of residence.