The solution is:
Edit
/plugins/tweet-this/tweet-this.php
and change line 89 from
define('TT_API_POST_STATUS', 'https://twitter.com/statuses/update.json');
to
define('TT_API_POST_STATUS', 'https://api.twitter.com/1/statuses/update.json');
March 2013 they will again change something, to we will have to change to …/1.1/…
See: https://dev.twitter.com/discussions/10803