I have found the second and last cause of my upgrading problems: there is a small bug in Model->save() which prevented the validation of the model fields. You find a patch on https://trac.cakephp.org/ticket/744. So, with that patch applied, all my tests run without failures. Hooray!
Update (2006-05-06): It transpired that the bug was in the advanced validation approach I use, and not in Model->save().