Let's use this thread to share information, knowledge -- and maybe some educated speculation -- about all aspects of the Google [link:] operator. The post from mt_biker is a solid foundation to build on.
1. I only see a small percentage of the links I know exist -- is that right?
Let's clear up the one big overriding factor from the start. In contrast to Yahoo, Google does NOT report on "all" links that they have in their index. Note the wording that mt_biker quoted above: "webpages that have links". That's it, and nothing more.
They're not going to report on everything, because with that data their algo is too exposed to reverse engineering. (That's some of the speculation I mentioned earlier.) A few years ago the [link:] operator did report only links of PR 4 or above, but that has changed. Now some of the most important high PR links will probably not be shown in the results.
So what you have in the Google [link:] operator is almost "for entertainment puposes only". The results are of little value for an in depth analysis -- but they do show you something.
2. Why does the link: operator so often return links from the domain being searched?
Because they fulfill the description. Pages on a domain often do link to other pages on a domain. But every page on a domain does not link to every other page on that domain -- so this isn't completely frivolous information.
3. With backlinks being considered so vital to good Google SERP's, are such "backlinks" of any value or should they be ignored?
Page Rank is defined by pages (read that as urls) and domains do not enter into it. So links within a domain do vote PR to other pages. Still, given the limitations mentioned above, you won't see them all, so if you do see one that is interesting or valuable in your analysis -- good for you. It won't happen every time.
4. Sometimes the [link:] operator returns absolutely no links, when I know for sure there are thousands. What's up with that?
Just an observation here, but this seems to happen around the time when new link and PR data is being exported from the secret back end of Google into the publicly available information. To date, some results have always come back to visibility, so I can only assume it's an artifact (occcasional bug) of the data push process.
[edited by: tedster at 4:35 pm (utc) on April 29, 2007]