This code

<script type="text/javascript">
<!--//--><![CDATA[//><!--
  var rwd_images = {
    widthBreakPoint: 480,
  };
//--><!]]>
</script>

are not inserted if the the setting widthBreakPoint blank.

Or is this a feature?

The minimum solution is, but not the final, to use proper variable_get() call.

Current
$widthBreakPoint = variable_get('responsive_images_widthBreakPoint', '');

Proper
$widthBreakPoint = variable_get('responsive_images_widthBreakPoint', 480);