Correction to the above -- it's actually 4 back links not 3. Also, maybe it's best if I provide a more detailed explanation of what I said above.
When most people place the validation link on their page they use the old school URI of validator.w3.org/check?uri=referer -- but that page does not exist on W3C, it's just a throw away reference and it can only be accessed by referral directly from your site.
If instead you use the new school way of understanding that it's all about conformance then you will use validator.w3.org/unicorn/ such as validator.w3.org/unicorn/check?ucn_uri=www.example.com%2F&ucn_task=conformance (me luvs unicorns).
When you see the validation result on the page W3C will provide a bookmark suggestion of:
validator.w3.org/check?uri=http%3A%2F%2Fwww.example.com%2F <------- Don't use this one it will only give you one back link.
Rather than simply use it as a bookmark, apply it as your link to them.
validator.w3.org/unicorn/check?ucn_uri=www.example.com%2F&ucn_task=conformance <------- This one forces a full conformance check and gives you 4 back links per valid page.
To get that URI above just copy it from the browser address window but DON'T FORGET TO CHANGE THE & TO & -- or else your code will become invalid, oh the irony of it all.
Now place that link on each valid page of your site and wait a few weeks for it to get indexed. Then go to Google and search your site by www.example.com (without the "site:" operator), and you will see a bunch of back links from W3C :)
I don't know why it is like this but by doing it this way your links from your domain persist on the W3C domain so that it appears as if it is a page on W3C rather than just a results page that gets thrown away after you leave. They then get indexed by Google.