EDIT: This has been solved by adding:
<link href="Skins/Office2007/Menu.Office2007.css" rel="stylesheet" type="text/css" />
When I click the filter icon on my grid, the menu pops up and I see a list of items, but there is no background to the menu.
My grid has EnableEmbeddedSkins set to "false". Whenever I set it to "true" it works, so the problem has something to do with that.
I am using the Office2007 skin, and I have all of the Office2007 images and the Office2007 CSS file inside the correct directory:
mySite/Skins/Office2007/
Thanks for your help.