I think I just found a bug in W3 Total Cache. I emailed W3 EDGE using their form, but figured I'd post here as well. Hopefully it's useful for someone.
I've got WordPress configured to http://www.eatingrules.com, and it normally adds the "www" if it wasn't typed in by the visitor... Working exactly as WP should.
However, when Page Caching (Disk Enhanced) is enabled, it breaks the forced "www" on the site's url. If someone goes to http://eatingrules.com, that's where they'll stay (the redirect just doesn't happen).
In Page Caching (Disk) mode, it works fine. As soon as I enable Disk Enhanced, however, the "www" is no longer added to the URL if necessary.
I'm running WP 3.2 and W3TC 0.9.2.3. Server is Apache, hosted on MediaTemple's Grid-Servce.