I installed Stanza on the iPad and tried to load the epub files into that. It failed, but stated that container.xml was missing. That was the right clue: I had created zip files from the modified text files that contained a directory, and that directory contained all the epub files: mimetype, META-INF with container.xml and OEBPS.
Repacking the zip with the files at the root of the archive brought order & peace back.
So iBooks was right after all. I have to take a look at what Sigil validated…
The validator that Mark mentioned has been installed by the IDPF and is available on their web page for online usage. Sure enough, it mentions that container.xml and mimetype are missing. Strange that calibre and iTunes accepted these files.
Last update: Sigil loads the malformed epub files, but saves them in the right format. I guess it validates the format stored in its memory.