What I did have a problem with was the way their payment page is not secure.
What page is that?
There's some weirdness going on with their SSL cert(s).
First the "Table Bookings" page brings you to some Business & Finance IE account on shared hosting at inet7.com. That cert shows up in Firefox as not being verified or encrypted (the more worrying issue). On closer examination, it's an Equifax cert (in date) and appears to be valid. So it looks like the Google Analytics code references "http" and not "https" (even though they give you code to automatically adjust!). It might be just that that's making Firefox diss the cert?
Secondly, the nominations page used a UserTrust.com cert (with Business & Finance as the O) on the goldenspiders.ie domain this time. Again, though, Firefox report site "not encrypted", but if you dig deeper it's only "Parts of the page..." and, again, it's the GA include code that's referencing "http://".
So maybe just fixing the GA includes would resolve the problems, but certainly both "secure" pages (where payment is accepted) are appearing as https and do have seemingly valid SSL certs behind them.