Try this, and see if it helps:
Qt Code: 
  1. MainWindow::MainWindow(QWidget *parent) :
  2.     QMainWindow(parent),
  3.     ui(new Ui::MainWindow)
  4. {
  5.     ui->setupUi(this);
  6.     selection=new QRubberBand(QRubberBand::Rectangle, this);
  7.     //setAttribute(Qt::WA_NoMousePropagation, true); //you are on a  top level widget!
  8.     //setAttribute(Qt::WA_NoMouseReplay, true); //what is this for here?
  9. }
  10.  
  11. void MainWindow::mousePressEvent(QMouseEvent * event){
  12.     MainWindow::mousePressEvent(event); //if you want the normal behavior to stay
  13.     selection->move(event->pos());
  14.     selection->resize(1,1);
  15.     selection->show();
  16.     event->accept(); //why ignore? you are using the event! at any rate, since in this case you have no parents for the main windows, it doesn't really matter.
  17. }
  18.  
  19. void MainWindow::mouseMoveEvent(QMouseEvent * event){
  20.     MainWindow::mouseMoveEvent(event);
  21.     qDebug()<<event->pos();
  22.     selection->resize(event->x()- selection->x(), event->y()- selection->y());
  23. }
  24.  
  25. void MainWindow::mouseReleaseEvent(QMouseEvent * event){
  26.     MainWindow::mouseReleaseEvent(event);
  27.     selection->hide();
  28.     event->accept();
  29. }
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