The web server at
https://btcmine.com/ is configured incorrectly. The issuer CA bundle is not being sent. This will be a problem for some browsers, but not others. Whoever provided you with the certificate should have provided a CA bundle, and you should configure your web server to send it along with your site's certificate.
I will look on to this. But right now I see problem only in one browser - Firefox 4.
Agreed.
It has had an update recently and the problem remains suggesting that they either don't know about a rendering defect, or there isn't one [many renders are patched to work with incorrect HTML that worked before on previous versions of browsers ... but nobody wants that to continue forever]. Either way, Firefox is a pretty large percentage of the browser community, even on Linux and Macs (and without looking, I am sure *BSD as well ... after all, the current MacOS is based on the code base of FreeBSD 3.x ... one of their worst releases oddly enough -- the irony!). There are no doubt ports for many UNIX variants.
I will install latest version of Firefox 3 on my other Windows 7 mining box [my Wife has her XP laptop locked or I would just the installation there] and see if it is specific to version 4.
If the fix is simple, it would be greatly appreciated. Otherwise, it really isn't that big of a deal for the time being. I use Chrome quite often for bitcoin related sites which all open when I launch the browser so that I can get to things fast and that avoids me having to have to do that with my primary browser which is Firefox 4 as that would be quite annoying watching about 6 tabs load at once on startup and a bit more slowly due to add-ins.

EDIT: Just tried with Firefox 3 and the site shows up just fine. I may just go back to using Firefox 3 on my machine until they get Firefox 4 straightened out (I would suspect adding HTML5 support and improving rendering performance introduced a defect that they have not yet found or fixed).