The option show W3C logos does show the logos for conformity. If you click on this logos normally this should check the source page for errors (referer). In my case source is https and the w3c is http. This will bring up an error message. I think it should link to https if source is https.
No Referer header found!
You have requested we check the referring page, but your browser did not send the HTTP "Referer" header field. This can be for several reasons, but most commonly it is because your browser does not know about this header, has been configured not to send one, transferred the referring document over a secure protocol such as https but is accessing the validator over ordinary non-secure http, or is behind a proxy or firewall that strips it out of the request before it reaches us.
This is not an error in the referring page!
Please use the form interface on the Validator Home Page to check the page by URL.
I have tried this with Google Chrome, Firefox, IE with the same result.
I believe the quick fix is to open the template files for editing - Tools, Skin developer, Edit skin files - and change all occurrences of http to https on lines 258-259 of index.htt and lines 382-383 of slide.htt.
But I have to wonder whether you really want to advertise the fact that your pages conform to a specification from 1999. HTML 4.01 is obsolete.
(BTW, the "promotional" links in the skin are also terribly outdated. Using them will invoke insecure resources, leading to a broken "lock" symbol on your secure pages. They can't easily be fixed, and shouldn't be used.)