Yep, the API documentation is gone; http://delicious.com/help/tools claims that developer documentation is coming soon. In the meantime, Pinboard's API almost exactly matches Delicious's, and its documentation is still up: http://pinboard.in/api.
Incidentally, the Delicious API is still working correctly (albeit slowly) for me.
I've also noticed that some of the RSS feeds I had previously subscribed to are starting to 404. I haven't had the patience to track down what the new URLs are, but no redirects? Really?
Email addresses with plus signs in the left-hand side now appear to be a new pain point. :P (My existing plussed-address is still in place, but any changes I make to my settings cause a server-side insistance that the email I've entered is invalid.)
So far, not impressed with the first steps Avos have taken, and I say this as a long-time fan of Delicious.