The book on the cover of which Cordelia finds the image of Der Kindestod also contains the passage on an unnamed demon belonging to the Brotherhood of Seven that Buffy and Sid defeated in The Puppet Show (1997).
This script was originally planned for the first season, before Angel became evil. It evolved into its aired form.
To this day, no one knows what "thing" on Buffy's face Cordelia was referring to. Suffice to say that it can be ascribed to jealousy - Cordelia is secretly envious of Buffy whom she sees as a rival, and has told herself that there is something wrong with Buffy, to make her feel superior, thus boosting her confidence. In past episodes, there were many instances of her criticizing Buffy's hair and skin while the adoring viewers clearly saw that there wasn't anything out of place, except for Cordelia being mean.
It has been conjectured that Der Kindestod may have been inspired by Freddy Krueger, the antagonist of A Nightmare on Elm Street (1984). However, Joss Whedon says that this character was "based on a 'this thing creeped me out as a kid' thing," as with many of the monsters on the show. In general, the monsters were suggested by the vague bogeyman figures that bedevil many children.