In a post by Jonathon Delacour, I learned about the differences between umlauts, diaeresis, and röckdöts.
A heavy metal umlaut is an umlaut over letters in the name of a heavy metal band. Umlauts and other diacritics with a blackletter style typeface are a form of foreign branding intended to give a band’s logo a tough Germanic feel. They are also called röckdöts. The heavy metal umlaut is never referred to by the term diaeresis in this usage, nor does it affect the pronunciation of the band’s name.
He also catches the New Yorker in an editorial slip-up:
In the Seymour Hersh article, the diaeresis is used not only in the word “reëlection,” but also in “preëmptive,” “coördinate,” and “coöperation.” Interestingly, “cooperating”—as in “Most have been cooperating in the war on terrorism”—appears without a diaeresis, which suggests either an editorial error or that the diaeresis is not used in a present participle.
Language Hat concurs that the omission of diaeresis in “cooperating” is an error, rather than an exception to the rule.