Imagine surfing Wikipedia, reading an interesting fact you'd like to remember, and simply clicking a button next to it that added that fact to your daily spaced repetition learning database.

Because WP is unstructured natural language, this is impossible to automate completely. It might be possible to automatically generate flashcards from something more structured like the entries in Freebase, but would you want to learn them?

If you are willing to do a little work, Supermemo has an idea of structured note-taking/editing, called incremental reading. SM has the most support for it, but really it's just copying the text into a text editor and expecting you to cut it down to notes and then to flashcards.

Also, while there are good spaced repetition programs/databases out there (like Anki), the databases aren't collaborative like a Wiki, and in general could be much better.

Agreed. If I were to tackle this, I would start with the Anki folks (Mnemosyne is too slow and conservative), and I would do something like write an Anki plugin to scrape a page inside a Category on a wiki (probably the card contents would be formatted using tables or templates), and then everyone just edits the page and any future downloads get the modified version. This wouldn't handle existing users getting updates, but that's the general problem of distributed revision control, which is certifiably Hard.

Actually, collaborative abilities aside, I think even a very well kept but closed database could be quite valuable (more so than Rosetta Stone or other such software for learning a language for instance).

I think all the commercial providers of flashcards for SM have failed. Apparently it isn't that valuable.