Keeping up apprearances
Having spent the effort to provide your visitors with a new updated site consider creating a tailored 404 page so if an error does occur they are presented with something in tune with your new design instead of something that could make them feel your new site isn't working.
Double check all your links to make sure that they are working – some of your older links out could just possibly be pointed to now closed sites and you may want to update links you have into your site, especially if you have changed domain or pages, as you certainly wouldn't want to lose any existing back links!
There are those visitors who don't like to see a lot of change and could even become confused with your updated site so ensure an easily accessible site map to try and assist this kind of visitor.