For those of you, like us, who reverting to compatibility mode or upgrading are not good solutions at this time, we have a JavaScript patch that has a dependency on jQuery.
One potential problem is that when a date or time picker element fades out, you can see the iframe behind it with the unstyled word "false" in it. Just something to bear in mind and watch out for if you decide to use this patch.
During our investigation, we also noticed that this version of RadDatePicker works fine IE11, just not IE10.