The audience for the CVs on StackExchange Careers Site is comprised of hiring managers and the like, though for a company of more than a few dozen employees, it's common for an HR person to do some initial screening. I have found these folks to be very conservative, as a group. In particular, these people, for better or worse, are accustomed to looking at CVs having a particular format--a format that has remained more or less unchanged for centuries (i believe it was the ancient Babylonians who invented the CV in its current form, but at present there is no consensus among scholars).
I do not think the SO Career Site CV format ought to be changed to accomodate those preconceptions--i am thrilled SO is trying to change them; however, i think adding a folding feature would make the SO format more accessible to these administrative types (who sometimes react to an unorthodox format by tossing it and moving on to the next one in the pile). And i don't think it will compromise the awesomeness of SO Careers.
In other words, the CV Sections--e.g., Technology, Experience, Education,..--could be initially folded in the main view then expanded one section at a time by clicking on the section name. If you know the Accordion Widget in the jQuery UI Library, then you know what i'm talking about.
Or for a rough (very rough) idea: