Three tips that I use:
1) Make sure you have a sitemap that's submitted to Google Webmaster Tools (and Bing's Webmaster Tools as well) and make sure that this sitemap is using all the correct URLs and non of the incorrect ones.
2) Add a plugin to Joomla that allows you to set (or have it be set automatically) a canonical meta element for your articles. Google and other sites will use that canonical value while indexing.
3) Periodically check Webmaster Tool for links that didn't get corrected from those first two tips. For any you find, set up a permanent redirect (ie, HTTP Code 301 redirect) from the non-SEF URL to the permalink/correct URL. Once Google starts hitting the redirect it'll update its index to go to the new location instead of the old one.
What's more, the non-SEF url does not work
This is because it's loading that article through your "homepage" menu item (because no other Itemid is set). Your template happens to be set up so that when the template is loading the homepage the template does not attempt to load the Joomla "component" block (ie, there is no
<jdoc:include type="component" /> set). Without the "component" block you're not going to see your article on the page.