B. Palin's reaction to that joke was hilarious but partially because the joke itself was so fucking lame and easy anyway. It was barely even a joke and made no sense; it was at best a passing reference with no real target in particular. Palin's actual kid is a male and much younger so it was clear that some writer just thought "down syndrome=Palin" and called it a day. This, when Palin is practically a fucking walking joke in herself. A legitimate attack on her actual politics, or for that matter her tendency to trot her child around as a political accessory (a point the "down syndrome girl" actress made herself in a statement much funnier and more spot-on than that Family Guy joke), would have been much funnier and actually possibly contained some edge. The only thing Palin's reaction proved is that it's possible for some people to be overly sensitive to even the most toothless joke. And most of the supposedly "edgy" jokes on Family Guy are, at best, just as toothless.
If you want edgy, don't watch The Simpsons and don't watch Family Guy. There are better programs than either of them that are still, legitimately, pushing the envelope and not just providing some cheap simulacrum of edge just to impress high school students.