This particular issue is not a matter of turning off and on Design Mode.  Design mode should only be hiding content, not the entire module or page.  Enabling/Disabling Design mode has made no difference for me in troubleshooting this issue.  Unless the Design Mode function is intricately tied with other functions of DNN, I don't think it's really the issue in this particular case.  If anything, it seems to be a caching issue.

In addition to my example above, here is another observation:  I changed the name of a page (tab) from "Support Us" to "Donations" using the page settings.  If I refresh the page, or visit other pages, I will notice the link in the navigation menu will sometimes say "Support Us" (the old page name) and other times it will say "Donations".  Again, once I restart the application, this behaviour stops and the new page name "sticks".  The same happens for any other settings I might change, ex: changing a module title, enabling printing on a module, setting view permissions on a page, etc. 

Lowering or turning off caching hasn't helped though, and actually resulted in my server's CPU usage to spike and the site ground to a halt.  Exactly as what happened to the dotnetnuke.com website last month: http://www.dotnetnuke.com/Community/Blogs/tabid/825/EntryID/1608/Default.aspx

I've just upgarded from 4.6.2 to 4.7.0 and this issue still exists.