Jquery UI selectmenu not working in dialog

The problem is that jQuery UI is generating the "drop-down" for the select on the page, but this is outside the div that becomes your popup. Then when the dialog is displayed, it covers the "drop-down".

If you move the selectmenu() call to after the dialog appears, it works correctly.

Your snippet updated:

$('.RegularDialog').dialog({
  autoOpen: false,
  modal: true,
  height: 500,
  width: 570
});
$('#OpenDialog').click(function(e) {
  $('.RegularDialog').dialog('open');
  $('select').selectmenu();
});
<head>
  <link href="//code.jquery.com/ui/1.11.2/themes/smoothness/jquery-ui.css" rel="stylesheet" />
  <script src="//code.jquery.com/jquery-1.10.2.js"></script>
  <script src="//code.jquery.com/ui/1.11.2/jquery-ui.js"></script>
</head>

<body>
  <div id="Dialog" title="Edit Dialog" class="RegularDialog">
    <form action="">
      <table>
        <tr>
          <td>Select the Type</td>
          <td>
            <select id="Type">
              <option value="a">Type 1</option>
              <option value="b">Type 2</option>
              <option value="c">Type 3</option>
            </select>
          </td>
        </tr>
      </table>
    </form>
  </div>

  <button id="OpenDialog">Open Dialog</button>
</body>