i've tried it here on different configurations and also have problems with firefox (tested with 10, 13 & 15). page load times were very slow initially (though this might have just been a hiccup) and search doesn't give a result but a generic category.

however i'm no web developer so i'm not sure what breaks the functionality of the site's search in firefox...

Thank you for that, I had a feeling my browser was actually working correctly! How do I report this directly to Firefox?

you could go to firefox > help > submit feedback... and report the site. although i'm not sure if this is a bug in firefox or a problem with the coding of the website.

Looks that is is caused by the HTTP/1.1 301 MOVED PERMANENTLY response.
Firefox doesn't seem to be sending the GET parameters to the new location and thus you get a generic page.

HTTP/1.1 301 MOVED PERMANENTLY
Content-Type: text/html; charset=utf-8
Transfer-Encoding: chunked
Connection: keep-alive
Server: gunicorn/0.14.2
Vary: Cookie
Location: http://shoply.com/marketplace/

So would that be a problem with firefox or the website?