In particular: In the second interval, both A and B should be flatted; in the third, there is no G# in the original tetrachord; in the fourth and fifth, there is no B natural in the original tetrachord; in the sixth, there is no A natural in the original tetrachord.

I'm also not aware of Webern or Schoenberg using this tetrachord much explicitly.  There might be a few of them here or there in their music, but I'm pretty sure it's not a significant feature of either's music (as it certainly is in Carter; I don't know about Perle).  I don't think either Webern or Schoenberg even knew of the special properties of this tetrachord.  The literature on Webern and Schoenberg that I know certainly doesn't mention this.  Mind providing citations?

Finally, the second "External Link" is dead.  It's also questionable: Carter's Night Fantasies is usually cited as the quintessential example of registrally deployed all-interval twelve-tone series, quite a different phenomenon than all-interval tetrachords.  There might be all-interval tetrachords within it, though - it'd be nice to have the link fixed so we can see!146.96.130.201