>I have an ASP.NET application running with Set Compatiblity On. If I run that application under HTML5, this is all messed up. If I turn that switch off, everything is ok. This is mentioned at many places on the net that this switch should be turned off in IE because it gives this result. Is there a way to turn that switch off from our application or we have to tell all of our users to turn it off?

I don't think you should control the way user's browsers are set up. Are you sure you're unable to fix your application for Compatibility Off ?