Failed font selection on Mac/Cocoa when there are multiple copies of a font installed (as reported by Font Book)

When Font Book on Mac OS X reports that multiple copies of a font is installed Qt will sometimes fail to select a font, for example:

#include <QtGui>

int main(int argc, char** argv)
{
QApplication app(argc, argv);

QFont invisibleArial("Arial", 12, QFont::Bold);
QLabel label("Foo");
label.setFont(invisibleArial);

QLabel label2("Bar");
label2.setFont(QFont("Arial", 12));

label.show();
label2.show();

return app.exec();
}

In my case I had Arial bold installed both in /Library/Fonts and /Library/Fonts/Microsoft. Both fonts worked perfectly on their own, but Qt would not draw the bold one until I manually disabled one of the instances in the Font Book application.