Even as the nuclear plant crisis in Japan is worsening, nothing about Japan is currently trending on Twitter, while Gilbert Gottfried has been trending off and on all day. People are evidently more worked up about someone telling jokes about Japan than they are about the crisis in Japan. I suppose this says something about a lack of empathy people subconsciously see in themselves--unable to confront it, they'll attack a scapegoat.
This seems to me part of society adjusting to being more connected. Twenty years ago, joking about a disaster occurring on the other side of the world might be slightly more of a faux pas than joking about the Civil War. But now we're instantly connected to Japan.
As for Gilbert Gottfried, the last thing I think he is is insensitive. You have to be sensitive to be good at making consistently insensitive jokes. That's what makes him funny. It's also why humour is a coping mechanism. He's sincere when he says he meant no disrespect, just as he really loves Groucho Marx.