There are all sorts of issues here.
First, there is the free speech issue.
"I've been getting a lot of e-mails about it, and I'm distributing them all," said Omary, a Damascus native who sells real estate in Northern Virginia. "There is a limit to freedom. There are 1.2 billion Muslims in the world. Let's have some respect."Is this true? We accept some limits on free speech but they mainly have to do with speech that creates danger (calling "fire" in a crowd when there is none), and slander. The list has gotten longer, though. Hate speech has been one of those limits for the last fifteen years or more. Universities have strong limits on hate speech but general limitations have not been imposed nor are they likely to be constitutional in the US.
The closest parallel in the US is flag-burning. It is considered protected speech (as long as you burn your own flag in a safe manner) but there has been a movement to pass a constitutional amendment banning it. Similarly, Moslems are putting together a petition to the UN to prohibit representations of Mohammed.
I am against both of these. Freedom of speech is an all or nothing proposition. It only counts if it includes speech that makes people uncomfortable.
Another issue is how far a country needs to go to keep its citizens from offending anyone else. The entire country of Denmark is being held responsible for the actions of one of its newspapers. Further, the main offense is not the contents of the cartoons, it is the cartoons themselves. Moslem law forbids representations of the profit. Can a religion demand that a secular nation follow this rule?
That brings us to the issue of how Muslims regard the rest of the world. Muslims have a long history of tolerating other religions but only in a subservient relationship. This has caused small-scale issues for years, especially concerning how women dress and act in public.
One frequently cited point is that Moslems would never show such disrespect to Jesus of Moses. This is a bit of trickery. The same laws that forbid representations of Mohammed also apply to Jesus and Moses. They do not character these religions because they recognize Moses and Jesus as part of their religion, not because they respect other people's religions.
Do Muslims say or do things that are offensive to the West? Americans who remember images of Moslems dancing for joy at the fall of the World Trade Center certainly think so. Then there is the Iranian museum housed in the former US embassy. In order to enter it you have to tread on a US flag.
How about this? A bit over a year ago Iran produced a TV series entitled Zahra's Blue Eyes. It showed Palestinian children being kidnapped and harvested for body parts for Israelis.
finally, I keep seeing about how insular the Americans are, how we don't understand world politics, especially in the middle east. The protests show that Arabs are less informed about the West than we are about them. There is a hidden assumption in all of the protests that newspapers in Denmark are controlled by the government. They is why protests include all things Danish. The protesters have no idea at all what freedom of the press really means.