A small script to help you fix the notice with a Drupal variable not being able to be properly unserialized. Make sure you have the devel module enabled for the dpm function used in the error handler.

detect_faulty_variables.php

<?php
set_error_handler(function($errno, $errstr, $errfile, $errline, $errcontext) {
  dpm($errcontext);
});
$variables = db_query('SELECT name, value FROM {variable}')->fetchAllKeyed();
foreach($variables as $name => $values) {
  $value = unserialize($values);
}
restore_error_handler();