So close... I installed the Anti-Splog plugin just now, and everything appears fine. No errors on install: API key, domain and IP address got the green "OK". Screens in Site Admin all appear without errors.
However, when you go to http://www.MY-WPMU-INSTALL.com/wp-signup.php and fill out the form, clicking "submit" does nothing. It doesn't go to the second page of the form where you specify the subdomain, etc.
So, as of now, nobody can register for a new blog. How can I fix this? If needed, I can provide the actual URL to the signup page.