On October 26, the Ubuntu team released a new version of Ubuntu, 6.10 (aka Edgy). I waited a couple of days for them to work out any last minute bugs, and decided to proceed with the upgrade today.
In the Ubuntu 6.10 / Edgy release notes, Ubuntu recommends the following procedure to upgrade from Dapper to Edgy:
# apt-get dist-upgrade && apt-get dist-upgrade
That will not work. Why? Because sources.list needs to be updated first (and apt-get update needs to be run beforehand).