Here's an interesting early instance of the expression, from Richard Corliss, "Movies: The B Movie Is Alive and Well... Thanks to Outrageous! and Citizens Band. Now for the Bad News," in New Times, volume 9, number 6 (1977) [combined snippets]:
Film critics are lazy creatures. They want to devote their column space to movies that will be seen, or at least talked about, by the largest possible number of their readers. They want to see films in comfortable, comforting surroundings: a plush screening room in the company of a few other movers and shakers, not a noisy movie house full of shovers and makers. They may even enjoy seeing some shards of their prose on a movie marquee, and find themselves sprinkling "money quotes" through an otherwise tepid review. And as the years pass they become more interested in what they're saying than what they're seeing; their profession is more important than what was once their obsession. (You'll notice I've cast this jeremiad in the third-person plural. Goodness knows I'm not guilty of any of these sins.)
The result: the movies you read about tend to be the ones most heavily prescreened and presold. You'll find millions of words knocking Exorcist II: The Heretic, but hardly a sentence praising—or knocking—a B-movie bijou like Special Delivery (Movies, NT, February 18, 1977). I sometimes think this benign neglect is a good thing.
The quotation that William Safire cites in his 2005 "On Language" column, as noted in Mark Beadles's answer, actually comes from a 1984 Time magazine review of C. David Heymann's Poor Little Rich Girl, not from the 1983 Barbara Hutton biography itself [combined snippets]:
Poor Little Rich Girl seemingly had everything going for it: a notorious beauty who died an impoverished recluse in 1979, a supporting cast if lovers that included Howard Hughes and James Dean, and a seasoned biographer, working from interviews with the heiress as well as her unpublished diaries. Random House was delighted but not surprised by the enthusiastic "money quotes" in early reviews. After all, the work had been chosen as a Book-of-the-Month Club alternate, Vanity Fair had excerpted a chapter, and the film rights had been sold for $100,000.
Richard Corliss was a film critic and editor at Time magazine for 35 years, starting in 1980, so he was working there when the review of Poor Little Rich Girl appeared, but I have no idea whether he had anything to do with that review. Corliss's 1977 review in New Times dates to his Film Comment days (1970–1980).
In any event, both the 1977 film review and the 1984 book review refer to "money quotes" in the sense of quotations that a marketing firm or publicist would highlight in advertisements, cover blurbs, or other promotional material to market the subject of the quotation. In short—and logically enough—a "money quote" seems in its earliest days to have referred specifically to a quotation extracted from its original context and used to sell the thing it talked about.