It seems that a disk has to appear on the desktop to allow dragging to the 'Cleaner' tab. I only have disks shown in the Finder Sidebar and they can't be dragged onto the Cleaner (result is, of course, removal from the Sidebar). Use Finder->Preferences->General to have disks appear/disappear from the desktop.

When you've selected the disk from the sidebar you can drag teh "proxy icon" to the cleaner section. The proxy is the icon to the left of the name of the volume in the title bar of the window - this item is "draggable".

I am unable to drag the "proxy icon" to the cleaner section. It refuses to accept it.

Works for me. You have to open the folder you have in the sidebar and then in the window displaying the contents of that folder drag the small icon left to the title(name) of the window to the prefpane. In the prefpane you have to drag it onto the harddrive symbol itself.