When a Frame is in full screen mode all modal dialogs open behind that frame. The dialogs do receive input focus but are painted behind the frame window.
This happens on Linux Mint 14 only and is reproducible with Oracle JDK 1.7 update 10 and also with OpenJDK 1.7

To reproduce run the code below. Then tick the checkbox to switch to full screen mode and press the button to open modal dialog. The dialog will open behind the frame window.

package javaapplication1;

import java.awt.GraphicsConfiguration;
import java.awt.GraphicsDevice;
import javax.swing.JDialog;

/**
 *
 * @author stan
 */
public class NewJFrame extends javax.swing.JFrame {

    /**
     * Creates new form NewJFrame
     */
    public NewJFrame() {
        initComponents();
    }

    /**
     * This method is called from within the constructor to initialize the form.
     * WARNING: Do NOT modify this code. The content of this method is always
     * regenerated by the Form Editor.
     */
    @SuppressWarnings("unchecked")
    // <editor-fold defaultstate="collapsed" desc="Generated Code">
    private void initComponents() {

        jCheckBox1 = new javax.swing.JCheckBox();
        jButton1 = new javax.swing.JButton();

        setDefaultCloseOperation(javax.swing.WindowConstants.EXIT_ON_CLOSE);

        jCheckBox1.setText("Full screen");
        jCheckBox1.addActionListener(new java.awt.event.ActionListener() {
            public void actionPerformed(java.awt.event.ActionEvent evt) {
                jCheckBox1ActionPerformed(evt);
            }
        });

        jButton1.setText("Show dialog");
        jButton1.addActionListener(new java.awt.event.ActionListener() {
            public void actionPerformed(java.awt.event.ActionEvent evt) {
                jButton1ActionPerformed(evt);
            }
        });

        javax.swing.GroupLayout layout = new javax.swing.GroupLayout(getContentPane());
        getContentPane().setLayout(layout);
        layout.setHorizontalGroup(
            layout.createParallelGroup(javax.swing.GroupLayout.Alignment.LEADING)
            .addGroup(layout.createSequentialGroup()
                .addContainerGap()
                .addGroup(layout.createParallelGroup(javax.swing.GroupLayout.Alignment.LEADING)
                    .addComponent(jCheckBox1)
                    .addComponent(jButton1))
                .addContainerGap(294, Short.MAX_VALUE))
        );
        layout.setVerticalGroup(
            layout.createParallelGroup(javax.swing.GroupLayout.Alignment.LEADING)
            .addGroup(layout.createSequentialGroup()
                .addContainerGap()
                .addComponent(jCheckBox1)
                .addPreferredGap(javax.swing.LayoutStyle.ComponentPlacement.RELATED)
                .addComponent(jButton1)
                .addContainerGap(231, Short.MAX_VALUE))
        );

        pack();
    }// </editor-fold>

    private void jButton1ActionPerformed(java.awt.event.ActionEvent evt) {
        JDialog dlg = new JDialog( this, "test", true );
        dlg.setSize(300,300);
        dlg.setDefaultCloseOperation(JDialog.DISPOSE_ON_CLOSE);
        dlg.setVisible(true);
    }

    private void jCheckBox1ActionPerformed(java.awt.event.ActionEvent evt) {
       boolean isFullScreenMode = jCheckBox1.isSelected();
        GraphicsConfiguration conf = getGraphicsConfiguration();
       if( null != conf ) {
           GraphicsDevice device = conf.getDevice();
           if( device.isFullScreenSupported()  ) {
                dispose();

                setUndecorated( isFullScreenMode );
               try {
                    device.setFullScreenWindow( isFullScreenMode ? this : null );
               }catch( IllegalArgumentException iaE ) {
                   iaE.printStackTrace();
               }
               setVisible(true);
           }
       }

    }

    /**
     * @param args the command line arguments
     */
    public static void main(String args[]) {
        /* Set the Nimbus look and feel */
        //<editor-fold defaultstate="collapsed" desc=" Look and feel setting code (optional) ">
        /* If Nimbus (introduced in Java SE 6) is not available, stay with the default look and feel.
         * For details see http://download.oracle.com/javase/tutorial/uiswing/lookandfeel/plaf.html 
         */
        try {
            for (javax.swing.UIManager.LookAndFeelInfo info : javax.swing.UIManager.getInstalledLookAndFeels()) {
                if ("Nimbus".equals(info.getName())) {
                    javax.swing.UIManager.setLookAndFeel(info.getClassName());
                    break;
                }
            }
        } catch (ClassNotFoundException ex) {
            java.util.logging.Logger.getLogger(NewJFrame.class.getName()).log(java.util.logging.Level.SEVERE, null, ex);
        } catch (InstantiationException ex) {
            java.util.logging.Logger.getLogger(NewJFrame.class.getName()).log(java.util.logging.Level.SEVERE, null, ex);
        } catch (IllegalAccessException ex) {
            java.util.logging.Logger.getLogger(NewJFrame.class.getName()).log(java.util.logging.Level.SEVERE, null, ex);
        } catch (javax.swing.UnsupportedLookAndFeelException ex) {
            java.util.logging.Logger.getLogger(NewJFrame.class.getName()).log(java.util.logging.Level.SEVERE, null, ex);
        }
        //</editor-fold>

        /* Create and display the form */
        java.awt.EventQueue.invokeLater(new Runnable() {
            public void run() {
                new NewJFrame().setVisible(true);
            }
        });
    }
    // Variables declaration - do not modify
    private javax.swing.JButton jButton1;
    private javax.swing.JCheckBox jCheckBox1;
    // End of variables declaration
}