Test usage of [com_ajax](https://github.com/joomla/joomla-cms/pull/1960). Please note I don't know how the jQuery response looks like, this is based on guess.

gistfile1.js

$.ajax({
	type : 'POST',
	data : request,

	// Got HTTP response code 200
	success: function (response)
	{
		switch (this.data.request.format)
		{
			// Handling JSON format
			case 'json':
				if (response.success)
				{
					// Do something with response.data
				}
				else
				{
					/* We got here because:
					 * a) developer didn't use proper query string
					 * b) called module/ plugin threw and exception
					 *
					 * Error message for debugging is in response.error.message;
					 */
					alert('Contact developer of this extension');
				}

				// There are some messages to show
				if (response.messages)
				{
					Joomla.renderMessages(reponse.messages);
				}
			break;

			case 'raw':
				// Update the element with received data
				break;

			case 'image':
				// Update the image with received data blob
				break;

			case 'xml':
				// Parse XML
				break;

			default:
				// This extension cannot handle other formats.
				break;
		}
	}

	// Any format but JSON
	/* We got here because
	 * a) developer didn't use proper query string
	 * b) called module/ plugin threw and exception
	 *
	 * Error message for debugging is in response.responseText.
	 * Additionally may check for HTTP status code: response.responseCode
	 */
	error: function(response)
	{
		alert('Contact developer of this extension');
	}