I just had a similar issue (June 2014) with Views UI. The ajax interactions on the 'style settings' simply stopped working so click on 'customize field HTML' and nothing happened. Hence finding this post/tip. I went to the Modules/JQuery configurations screen (http://website.co.uk/#overlay=admin/config/development/jquery_update) and instructed the Admin Pages to use JQuery v 1.5 (instead of the current 1.10). All View UI interactions then worked fine again.
Adding this extra note for anyone that might find that handy. Thanks to Vintorg and other repliers for the solution.
Mystery solved. It looks like a conflict with what version of jQuery I'm using. On the site that isn't working, I have jQuery update set to 1.7 (which the slider depends on). The site that works didn't have jQuery updater, and seems to be running v1.4. So, I dropped the version of jQuery from 1.7 to 1.5, and views is back to normal (but, of course, the slider doesn't work).