Yes, we are talking about Pages.
I did not change any templates during the upgrade. WP worked fine before the upgrade. Page.php is in place, index.php too.
Somehow this seems to be linked to my pages hierarchy: I’ve just noticed that if the page has no parent page, it will show fine. But if I place the page in my hierarchy of pages, it will break.
If I change my Permalink structure to Standard (was using Day and Name), the Page shows up okay as well. Did I somehow screw up my Permalinks?