I've found a workaround here:
http://getserver.de/bugs-fixes/12-joomla-3-x-finder-plugin-verursacht-fehler-beim-speichern-eines-beitrages.html

Translation for the non german here:
Error Message

Speichern fehlgeschlagen! Fehler: Column count doesn't match value count at row 1 SQL=INSERT INTO `jos_finder_tokens` (`term`,`stem`,`common`,`phrase`,`weight`,`context `,`language`) VALUES ('impressum', 'impressum', 0, 0, 0,6, 1, 'de') 

note the 0,6 that is not quoted.

The Autor noted that this is a issue with the Hosting envoirment (LOCALE) that can be fixed by.
dpkg-reconfigure locales (<-- Debian)

Or by code here: administrator/components/com_finder/helpers/indexer/driver/mysql.php Line: 602
Old:

. (float) $token->weight . ', '

New:

. (preg_match('/,\d+$/', $token->weight))?str_replace(array('.', ','), array('', '.'),$token->weight):str_replace(',','',$token->weight) . ', '

btw: Both solutions did not work for me, I did instead:

. str_replace(',', '.', $token->weight) . ','

See the fix in #5318