An opaque DragImageComponent (one that returns true for IsOpaque()) does not redraw correctly. As it is dragged over a non-Juce window, if the non-Juce window paints the painting happens over the heavyweight peer for the DragImageComponent, and the DragImageComponent is not refreshed (it picks up goobers).
The problem is caused by the ComponentPeer::windowIgnoresMouseClicks (line 444 of juce_DragAndDropContainer.cpp) setting the WS_EX_TRANSPARENT style on the window during addToDesktop().
Removing the windowIgnoresMouseClicks flag from the frame eliminates the goobers however I don’t think this is a proper fix.
To demonstrate the problem reliably, adjust the demo application so that it produces a DragImageComponent that returns true for IsOpaque (this could happen on systems without layered window support or by commenting out the test for canUseSemiTransparentWindow in juce_DragAndDropContainer.cpp). Run the Task Manager and select the processor usage display graph. Run the juce Demo application, go to the Drag and Drop demo page, drag a row from the list and move it over the area of the Task Manager that is refreshing (the graph). Result: the drag image will pick up goobers.