Here's a workaround: select a track in the library pane in Clementine, then drag it towards the left side of the screen, 'pushing' the launcher away. The launcher should disappear, and might behave ok for a little while longer. The problem sometimes is that after this trick, it is difficult to get the launcher to appear long enough when you really want it. So the workaround for the workaround is: play around with the launcher until it works. (For instance, get into another app like Firefox, select and drag text to the Ubuntu logo in the top left corner.)

I think the bug in Clementine happens when you drag a track to the playlist, so try double-clicking the track instead. (In fact, I get the same bug in several other apps when I try to drag and drop files or text).