[...] Except for the ironic-idiom case, the only time it's correct to use all of is when the adj. phrase is folowed by a pronoun--"All of them got cards"; "I wanted Edgar to have all of me"--unless, however, the relevant pronoun is possessive, in which case you must again omit the of, as in "All my friends despise Edgar." [...] With all plus a noun, it turns out that the medial of is required if that noun is possessive, as in "All of Edgar's problems stem from his childhood," "All of Dave's bombast came back to haunt him that day." I doubt I will ever forge this.
the ironic-idiom case being "Sex with Edgar lasted all of a minute"
incidentally, this has inspired the idea of a putative grammatical lesson (or something of the sort) that really tells a story through the examples that are given (which DFW explores briefly in this paragraph)