First of all, there is no more against portraiing Mohammed as a non-muslim than not worshipping (or even eating) cows as a non-hindu. Muslims should tolerate that as much as hindus do.

To clarify this, I dont't hate normal/moderate/peaceful muslims. But I don't like terrorists, and we shouldn't let them take away our freedom of speech.

About the Quran justifying terrorism: I admit that I never read the Quran myself (I don't have the time for that, at least atm) but I read the following from various sources:
There is a sura that forbids you to kill (but as in the Bible there is the problem that it might only mean don't kill other muslims). And there is an other sura that explicitly forbids you to kill yourself ("You shalt not destroy yourself").
But, in some parts of the Quran the it does tell you to kill infidels (but I don't know in which context). This includes a backdoor to terrorism, because there is a sura that tells you that it if you kill infidels, it does not matter if you kill yourself. This seems to justify terrorism inthe eye of terrorists. Furthermore, it becomes attractive, because when killing infidels you can escape judgement and get straight to heaven and get 72 virgins (but the arabic text is ambigious, it could also mean 72 white raisins ).
That's how I understood it. Quadraxas (or any other muslim), if anything of this is incorrect, just tell it, I'm eager to learn^^.

But about Islam being violent, what about this?:
http://www.youtube.com/watch?v=VselUW4Aoxg
Later in the full video (search for "The Big Debate"), the muslim scholar admits that in a muslim country, the penalty for apostasy is still death.

About the Mohammed cartoons in 2005:
In "The God Delusion" I read that some muslim who saw the cartoons in Denmark brought it to the muslim public world and added some more, offending pictures to it, including a gorilla that has nothing to do with the cartoons.
But even considering that they got a more "offending" version of the cartoons, this is no excuse for the violence that followed. Expression of free speech was followed by violence. Also, you should have some humor and be able to laugh about caricatures of your own religion. People ridicule about politicians and even other religions all the time and no one gets violent. In christianity, it's forbidden to make a picture of god and this has also happened and no one ever complained.

Also, I somewhere read that you could consider terrorists and parts of the islamic world as 500-1000 years behind in religious development, which means, they are on the stage of crusaders and whitchburners. Maybe an interesting thought. I dunno^^

http://www.brogames.de/Mohammed.jpg