Answered my own question ... an email showed up from Apple telling me how to install/synch iCal with the new beta. The email contains a link to web page with instructions; unfortunately they did not solve my problem. Everything detailed on the web page was already set up exactly as shown, since I've been a MobileMe member from the early days of ".Mac". But here's what fixed my problem:
Even though my MobileMe panes were all set up correctly, and I could "sync" in the MobileMe "sync" tab, no events were showing up. I ran software update and, lo and behold, there was a "security update" that had just shown up, so I installed that (plus the accompanying iTunes update or whatever it was). iCal still didn't work. But then, upon starting iCal, I got a dialogue box telling me that my user name and/or password was not being accepted by the server (even though it was working fine in the MobileMe system preferences panel). In iCal, I went to "Preferences" and then to "Accounts" and noticed that my user name had been entered for me (correctly), but my password had not. I entered the password, quit iCal, restarted iCal, and waited. Within a minute or so, things were whirring, and after a few minutes, all my events were back, but my groups were gone, as warned. (Not a big deal, as far as I can tell.) Just wondering why Apple didn't tell me to look in the "Preferences" menu in iCal in the first place. (Or why the info wasn't all entered automatically, since some of it was ...).
All's well that ends well ...