Ok, try this: First, reupload all the QuoteIt! files and reinstall the product (do not uninstall it first). Then run this query (replacing $TP with your table prefix):
[sql]UPDATE $TPdatastore SET
data = ""
WHERE title = "quote_settings"[/sql]
Finally, go to the language manager and save a language (you don't have to edit it). This will reset all the options and you can try saving it again.
If all that doesn't work, then I have no idea what's wrong, but you could use this workaround to make sure moderation is enabled:
In includes/functions_quoteit.php, find this
PHP Code:
$quoteitoptions = array_merge($mainsettings, unserialize($vbulletin->languagecache['quoteit_settings']));
and after that, add this
PHP Code:
$quoteitoptions['moderatequotes'] = 1;