When running jQuery Ajax requests, you can catch server related code errors by using the statusCode object:

$.ajax({
  url: 'script.php',
  type: 'GET',
  dataType: 'json',
  statusCode: {
    404: function() {
      $("#response").html('Could not contact server.');
    },
    500: function() {
      $("#response").html('A server-side error has occurred.');
    }
  },
  error: function() {
    $("#response").html('A problem has occurred.');
  },
  success: function() {
    $("#response").html('Success!');
  },
});