MT problem tracked down
I finally tracked down my problem with the post three days ago:
Because of an unknown reason if the title starts with "Advert" the entry gets no date through the <$MTEntryDate$> tag. There are also no links in all indexes, archives or on the next-/previous-links on the individual entry pages.
Well, I changed the title on that entry from "Advertisement" to "An advertisement" and everything is working again.
Strange. Found also no documentation or any sign of such behaviour on the internet. Am I the first one who recognizes this or is that the result of a plugin? Don't think so...