Good questions.
I have been born and raised here (chicago) so I have an understanding of both perceptions.
In Islam, any depiction of their prophet is strictly forbidden (says the quran). So first of all they create a picture of him, and secondly make a mockery of it and that is all fine. The main issue here is mentalities.
Here is America it was never an issue, and personally I got a chuckle out of it. Back in those parts of the world, its a different situation
We are dealing with third world mentalities and people who have minimal to no education. These are rundown places with really nothing to do, but say preach a religion. And there they take religion VERY seriously. Serious to an extent that they would kill for it (no pun intended) There is no concept of free speech and if you do try to voice your own opinion, you might get shot, its pretty rough.
To a non-muslim, its no big deal. To an extremist, he gets really upset and goes to his corner store to pick up an AK-47 for the price of a couple chipotle burritos (yummy). Note I say extremists, because typical muslims are not like that at all. In fact violence is not tolerated (says the quran) but is allowed only in retailiation. Sort of like if someone walks up to you and punches you, you can punch back in defense. So the muslims feels their religion was disrepected and they are 'fighting back'
Some say that if a similar comical mockery of Jesus was published (USA today, TIME) there would be a similar reaction. I dont think that would be the case, because Christians dont take religion to the extent to kill for and we do things differently here, in a more civil fashion.
The question is, why are they so easily agitated over something so petty? I bet the cartoon were half the problem, the other half is these people being on a high defense mode. Kinda of like high strung wife, she will snap at anything :rolleyes. Especially after 9/11 there has been an increase of discrimination towards muslims and they feel everyone who is not muslim is out to get them. They have to 'fight' against anything said or done against them. Especially the way media protrays them, because believe it or not, only a small percentage of them are the trigger happy type and those are the only ones you will see on thenews.
But in general they are short tempered people, kind of like the Italian mob who will gun you down over a deal gone bad.