We have a multilanguage website with approximately 50 subsites, running 1 copy of the Drupal software and several databases. After upgrading the core and all contributed modules to the latest recommended releases, we were locked out of all the sites with the message "The website encountered an unexpected error. Please try again later."
After some investigation, we pinpointed the problem to the Entity Translation module, and found that emptying the cache solved the problem. For the majority of the websites, we were able to go directly to www.example.com/admin/config/development/performance and hit the "Clear all caches"-button. For some sites, however, we got the "The website encountered an unexpected error."-message even here. The solution was then to downgrade to an older version of Entity Translation, go to www.example.com/admin/config/development/performance, upgrade again to 7.x-1.0-beta2, hit the "Clear all caches"-button and run update.php.
No action is really required here, but the trick mentioned above may help others encountering the same problem.