Content : Check grammar and spelling.
W3C : Ensure site is W3C compliant. View on multiple browsers.
SEO : Ensure SEO meta data is included on all pages / posts. Ensure site visible to search engine.
Sitemap : Don’t forget to create and publish a sitemap.
Google Webmaster : Submit your site to google webmaster tools.
404 Pages : Ensure you have 404 pages and that they work.
Legal Pages : Have a privacy policy, terms and conditions and disclaimer(s).
Contact : Have a contact page. If using a contact form, test it.
Social Media : Provide links to your social media web properties.
Navigation Menus : Test navigation. Get feedback on ease of navigation.
Links : Test all internal and outbound links. Broken links = BAD
Load Speed : Upon launch, test load speed. Improve if > 2 seconds.