I just "upgraded" from 3.5.3 to 3.6.7 but I had to manually install 3.6.7 and then just activated the new theme. Of course I had to move files to get the new theme to display as my old one was. Fortunately not too much custom code.
One thing I've noticed, besides the fact I have to re-assign my menus in the menu settings page, is that the header images no longer show the overlay I've set on the left/right hand side. See http://continuekimsfight.com for example. As the page loads, you see it flash up, then goes away. Is this a known issue? Maybe a settings change?