This post is on behalf of JDL, who wants to know how widely the phrase good shuts is used. It was certainly used in Derby when we were young, but is probably not confined to that area. It doesn’t appear in the OED or in Wright’s dialect dictionary.
It is used in the same way as good riddance is used. So one might say: Good shuts to that idiot!. A word of warning to non-native speakers — it is not very polite!