Hi Allan,
I just encountered that there are errors on the mentioned example page (http://www.datatables.net/release-datatables/extensions/ColVis/examples/jqueryui.html) which prevents it to render correctly.
Two files you include are not available at the given URL:
http://www.datatables.net/release-datatables/extensions/Plugins/integration/jqueryui/dataTables.jqueryui.css
http://www.datatables.net/release-datatables/extensions/Plugins/integration/jqueryui/dataTables.jqueryui.js
Regards