Hi Gorgon, this was a tough one
it's the first time this issue ever came up with our plugins.. It's not specific to Joomla. Our WordPress 360 product viewer would do the same if it was running on your Apache server with the same configuration. The issue and solution are summarized on this page: http://tkurek.blogspot.com/2013/06/252f ... pache.html
In short, your server has at least one URL rewrite rule configured to strip off ".html" from the page URLs. The rewrite rule in Apache "double-encodes" slash symbols (/) in the URLs we use for launching the popups with 360 product views and it breaks the URLs as shown in the linked post. This may also affect other functions in your Joomla setup (not sure).
Do you have access to your .htaccess where the Apache rewrite rule is configured to make the small adjustment as per the link above? We can assist with this if needed.