The brief backstory: The Post is a right wing rag and has always been pretty well hated by New York's black community (see, for example, Public Enemy's "Letter to the New York Post"). During the Clinton administration, News Corp got a waiver from the FCC that allowed it to own and operate multiple TV stations and newspapers in the NYC market. At the time, Jesse Jackson was perceived as having some pull with the FCC; therefore, News Corp had to play nice with Jesse and Rev. Al during the Clinton years.
Once little Bush came in, though, News Corp was once again cozier with the administration than Jesse and Co. were, so they were able to go right back to their normal state of outright hostility towards black liberals. Now, Al's strategy is to use the cartoon controversy as an excuse to ask the FCC to review News Corp's waiver.
Could that really work? The FCC will naturally be somewhat less dick-riding to News Corp under Obama than it was under Bush, but this still sounds like a stretch. My sense is that this is just a bargaining chip, which could end up making Al Sharpton look foolish if it totally fizzles out. But that could just be leftover pessimism from the past eight years.
Media beef-starter Michael Wolff actually thinks that Post editor Col Allan is going to get canned for this whole cartoon thing! If News Corp really was in danger of losing its waiver, then it certainly wouldn't hesitate to throw the greasy Australian editor overboard. And the NAACP would certainly be satisfied with that. But it would seem more characteristic for News Corp to just say "Fuck you" to black New Yorkers and forge ahead as usual. That's what makes them so fun, and evil!