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If the site ranks well and there's any way to preserve the present URL structure, that would be your best bet. If that's not possible, 301 the old URLs to the new applicable pages.

You can do this via .htaccess like this:

301 redirect /old-permalink-here http://new-full-url-goes-here

SEO Moz probably missed it because the inbound link is no longer active. Did you pull this error from Google Webmaster Tools? Check the date. It may be a very old error. Either way, implementing a 301 is your best bet.

I have not seen many (or any) examples of Google displaying duplicates. Is it your home page that ranks in the natural results right beneath the Local results? The "Places" results, generally speaking, will match the "Local Search" box that appears in local-based queries.