You would use IE11 in compatibility mode for an intranet that has a couple of sites that need compatibility mode to work. Unfortunately the way to do that is by domain name, so any sub domain gets caught under that umbrella.
The way to tell if the browser is in compatibility mode in IE11 is through the user agent string. There is a part of the string that gives you the rendering engine. For IE11 in compatibility mode that is Trident/7.0. IE 10 uses 6.0 or 5.0. The 5.0 is also used by IE9 so that could still cause issues with IE 10.
