Summary: call "list.setFocusTraversalKeysEnabled(false);" in the constructor of org.gjt.sp.jedit.gui.CompletionPopup to make it possible to use TAB for completion selection, in the same way as ENTER.
This currently doesn't work because TAB is used for component traversal by the focus subsystem and is thus never passed to the JList.
Reference: http://docs.oracle.com/javase/tutorial/uiswing/events/keylistener.html (read the "Version note"
Env.: jEdit 5.0.0, Oracle Java 1.7.0:15 on OS X (though this should apply since JDK 1.4 and to all platforms)