it should be possible to select text of the displayed JasperPrint with the cursor in the JRViewer. This should be activated (similar to other programs like Adobe Reader) by activate the "Select"-Mode via some Icon (RadioButton) in the toolbar. When this mode is selected the cursor should turns into a "Text-Selection-Curser" and it should be possible to select a Text like in other Programs.
During this Mode it is of course not possible to scroll through the document only by pressing and holding the mouse.
The highlighting of the Text usually works with the TextLayout: