If I have Windows running full screen on the second desktop I can click a file in Finder and then, with the mouse button held down, press Ctrl + right to slide to the Windows screen and drop it in Explorer to copy it from Mac to Windows. I can't seem to do the same to drag files from Explorer back to Finder. Copy and paste for files doesn't seem to work at all between Windows and Mac. Is this a limitation, or is there a setting to fix this? Using Mac OS X Lion, Windows 7 (NTFS).
Did you try the same in different view modes? Please try Window mode and try to reinstall Parallels Tools from virtual machine menu --> reinstall