Well, despite how tempting it is, it's important to realize that the groups that do this are not the same as the muslim community at large. In a way these actions are a convenient way of finding out who are extremists and who aren't. They have no right to tell what should be legal and illegal in countries others than their own - we won't infringe press freedom. The question is whether the pictures are insulting and harassing in a way that could be seen as illegal by existing law. Can anyone who is good at Danish law practise comment on that? With fairly international law concepts it could be seen as threatening and generalizing in a discriminating way to imply that the Prophet would be a terrorist, on the other hand showing such a picture in a collection of other pictures means the intended interpretation of the whole is more likely intended to not be concentrated on that single picture, but instead by reading the entire message the pictures, and the accompanying text, tries to convey. No matter what, it's according to western law only a borderline case of crime, if sentenced the sentence would be very low. It's important to point out that similar insults to Christian faith have been given, and not punished, in the same countries. Therefore, it's not a case of discrimination of muslim faith, but the way our laws work. However I can understand it's difficult for the muslims who feel offended to realize that, or even obtain such information at all. It's not appropriate to react with hate demonstration so early, before even getting the full knowledge about what happened. For example some demonstrants burned flags of many other countries than Denmark, then in the afternoon the same day said "oops, we got the wrong flag, but we love your nice country so don't worry, we won't harm you". It doesn't give a very serious impression... Plus it's also not very serious to burn the flags of a nation that has little to do with a newspaper in the country publishing something. Burning the flag of a nation is to say that your hatred is directed towards that entire nation, and every human being living in it.

It could be that it's just a temporary reaction and demonstration as a form of entertainment to have something to do. It could be that the entire thing is of the same kind as "we got the wrong flag, don't worry we didn't mean it" and that it'll go away soon. Or it could be, in the eyes of some extremists, an excuse to carry out terrorist actions towards Denmark and other countries (including those whose flags they accidentally burned due to lack of proper information at first). I think it'll become apparent in a month of so from now which way it is.