Qt supports an attribute named Qt::WA_TransparentForMouseEvents which will make mouse events pass through the widget with this attribute set. This is a very useful feature in many cases. Unfortunately this attribute only work for child widget but not for top-level widget. I hope Qt should make this attribute work for top-level widget too.
At least in windows, to make Qt::WA_TransparentForMouseEvents works for top-level widget is very simple, set WS_EX_LAYERED | WS_EX_TRANSPARENT to a window's extra style is enough. But I don't know what is needed for X11 and Mac.