Got this to work in IE9 by installing YUI 2.9.0. Seems to work fine with or without Compatibility Mode enabled. Here's how I installed YUI 2.9.0:
1) Download yui_2.9.0.zip from http://yuilibrary.com/downloads/, extract, and copy the build folder into a new folder: [moodleroot]/lib/yui/2.9.0
2) Download config_2.9.0.php from https://github.com/yui/phploader/blob/master/lib/meta/config_2.9.0.php and copy it to [moodleroot]/lib/yui/phploader/lib/meta/
3) Download json_2.9.0.txt from https://github.com/yui/phploader/blob/master/lib/meta/json_2.9.0.txt and copy it to [moodleroot]/lib/yui/phploader/lib/meta/
4) Edit [moodleroot]/lib/setup.php around line 202. Change
$CFG->yui2version = '2.8.2';
$CFG->yui2version = '2.9.0';
5) Not sure if necessary, but I purged all caches.
Drag-and-Drop ordering questions now work in IE9. Hopefully upgrading yui to 2.9.0 didn't break anything. We've got Moodle 2.0.3 on Windows Server 2008 R2 (IIS7 and MS-SQL 2008 R2).