Previewing an entity in the WYSIWYG does not add any attached styles or javascript from the AJAX callback

          var request = {};
          request['value'] = element.getOuterHtml();
          jQuery.ajax({
            url: Drupal.url('entity-embed/preview/' + editor.config.drupal.format + '?' + jQuery.param(request)),
            dataType: 'json',
            async: false,
            success: function (data) {
              element.setHtml(data.content);
            }
          });
          return element;

Our ajax request only loads the HTML part of the response. If a rendered entity adds CSS or JS that isn't yet loaded on the node page, this will make it appear broken in the WYSIWYG preview. yched is going to helpfully provide us with an example of what he had to do to get those assets loaded.