Ejemplo reproduciendo el problema

Código

      <object width="590" height="332">
          <param name="allowfullscreen" value="true" />
          <param name="allowscriptaccess" value="always" />
          <param name="movie" value="http://vimeo.com/moogaloop.swf?clip_id=13026281&amp;server=vimeo.com&amp;show_title=0&amp;show_byline=0&amp;show_portrait=0&amp;color=ff9933&amp;fullscreen=1" />
          <embed src="http://vimeo.com/moogaloop.swf?clip_id=13026281&amp;server=vimeo.com&amp;show_title=0&amp;show_byline=0&amp;show_portrait=0&amp;color=ff9933&amp;fullscreen=1"
                    type="application/x-shockwave-flash"
                    allowfullscreen="true"
                    allowscriptaccess="always"
                    width="590"
                    height="332">
          </embed>
        </object>
      

Ejemplo con la propiedad z-index

Código

      <ul class="submenu" style="display:none;position:absolute;z-index:2">
        <li>Submenu1</li>
        <li>Submenu2</li>
        <li>Submenu3</li>
        <li>Submenu4</li>
        <li>Submenu5</li>
        <li>Submenu6</li>
      </ul>
      <object width="590" height="332" style="position:relative;z-index:1">
          <param name="allowfullscreen" value="true" />
          <param name="allowscriptaccess" value="always" />
          <param name="movie" value="http://vimeo.com/moogaloop.swf?clip_id=13026281&amp;server=vimeo.com&amp;show_title=0&amp;show_byline=0&amp;show_portrait=0&amp;color=ff9933&amp;fullscreen=1" />
          <embed style="position:relative;z-index:1"
                    src="http://vimeo.com/moogaloop.swf?clip_id=13026281&amp;server=vimeo.com&amp;show_title=0&amp;show_byline=0&amp;show_portrait=0&amp;color=ff9933&amp;fullscreen=1"
                    type="application/x-shockwave-flash"
                    allowfullscreen="true"
                    allowscriptaccess="always"
                    width="590"
                    height="332">
          </embed>
        </object>
      

Ejemplo solucionando el problema

Código

      <object width="590" height="332">
          <param name="allowfullscreen" value="true" />
          <param name="allowscriptaccess" value="always" />
          <param name="movie" value="http://vimeo.com/moogaloop.swf?clip_id=13026281&amp;server=vimeo.com&amp;show_title=0&amp;show_byline=0&amp;show_portrait=0&amp;color=ff9933&amp;fullscreen=1" />
          <embed src="http://vimeo.com/moogaloop.swf?clip_id=13026281&amp;server=vimeo.com&amp;show_title=0&amp;show_byline=0&amp;show_portrait=0&amp;color=ff9933&amp;fullscreen=1"
                    type="application/x-shockwave-flash"
                    allowfullscreen="true"
                    allowscriptaccess="always"
                    width="590"
                    height="332"
                    wmode="transparent">
          </embed>
        </object>