An odd discovery today – if you don’t specify a protocol in your links, the browser apparently suppose it’s the same (be that http or https) as the current page. You can se it in action on Slashdot by viewing their source – none of the regular links has protocol specification – they just start with two slashes and the hostname (ie. //netfactory.dk/). In the case of Slashdot I suppose they don’t use it to save bandwidth, but in most cases it’s probably useless.
There are quite a large number of tools available for testing and checking a website, but the most valuable is (without doubt) the Web Page Analyzer – as it does tell (and help) you optimize your site in ways you may not have thought of. I am assuming that the site in question is either valid HTML (as any good site should be) or at least tested and found working in the browsers it should work in.