Starting with the 3.11 API the overviewmap dijit doesn't work in IE8 or IE7.
Try the sample for this to test.
It's giving me the following error:
TypeError: Unable to get property 'id' of undefined or null reference
Has anyone else run into this or have any ideas? It looks like the dojo version changed from 1.9.0 to 1.10.0 at the 3.11 release.
I ran a quick test and you are correct it looks like something broke with the update to 3.11. Can you submit this to Esri Support?