Just discovered that the effect in KDE 4.6.0 reported by the OP only occurs when you change the mouse option from single click to double click (Kickoff > System Settings > Input Devices > Mouse > General | Double-click to open files and folders). If you switch it back to single-click you can click on file and folder icons again and drag them around, allowing you to copy-and-paste or move them. KDE, eh?!
Anyway, I assume from the aforementioned bug report that KDE 4.6.1 will work correctly irrespective of whether single-click or double-click is selected in System Settings.