return false; - ignoruje

<script type="text/javascript">
<!--

  function processForm()
  {
    $('submit').disabled = true;
    $('submit').value = "Proces.  Prosím čakajte...";

    $('contact_form').request({
      onSuccess: function(transport)
      {
        if(transport.responseText.match(/^OK/) != null) {
          alert('Your message has been sent!');
          $('contact_form').reset();
        } else {
          alert(transport.responseText);
        }

        $('submit').value = 'Send Message';
        $('submit').disabled = false;
      }
    });

    return false;
  }

-->
</script>

   <form id="contact_form" action="process.php" method="post" onsubmit="return processForm()">
      Váš kontaktný email:<br>
        <input type="text" name="odos" size="30"><br><br>
      Predmet spravy:<br><h5>Krátky popis o akú chybu ide.</h5>
        <input type="text" name="predmet" size="30"><br><br>
      Text spravy:<br><h5>Opísani problému či chyby. Prosím čo najpresnejšie.</h5>
        <textarea rows="5" cols="40" name="text"></textarea><br><br>
      Opíšte kód z obrázka:<br>
        <img src="securimage/securimage_show.php" alt="CAPTCHA Image"><br>
        <input type="text" name="code">
        <input id="submit" type="submit" value="Odoslať">
    </form>