The window looses focus after it is shown in full screen and then calling showNormal().

It would be expected that the window would be in focus after this call.

Reproducible with:
#include <QtGui>
#include <QDebug>

class CustomWidget : public QPushButton
{ Q_OBJECT
public:

QMainWindow * m;
CustomWidget(QWidget* parent=0) : QPushButton(parent)

{ connect(this,SIGNAL(clicked()), this, SLOT(aSlot())); }

public slots:
void aSlot()

{ qDebug() << "aSlot invoked"; m->showNormal(); }

};

#include "main.moc"

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

CustomWidget wid;

QMainWindow m;
wid.m = &m;
QPushButton b("button...", &m);
m.setCentralWidget(&b);

QObject::connect(&b, SIGNAL(clicked()), &wid, SLOT(aSlot()));
m.show();
m.showFullScreen();
return app.exec();
}