Hi Thomas,
It took me quite some time to identify the real error behind the recaptcha issue and I finally found it after I've disabled the following plugin on your site, System - Open Graph Protocol. Below is the error that got generated when I'm trying to post a comment with recaptcha,
Warning: file_get_contents(): https:// wrapper is disabled in the server configuration by allow_url_fopen=0
It seems like your server did not enable allow_url_fopen as you can see from your backend > system > system information > php information,
http://screencast.com/t/c9No7WnNTCdP hence komento does not able to fetch the content returned by google recaptcha api. Can you consult with your webhosting provider and ask them to enable "allow_url_fopen" and then clear all the cache on your site and see how it goes?