There are some things that clearly disturb the general public to the point where the police are justified in stopping as it is happening due to the specifics of the situation but which should not be criminal offenses thanks to the First Amendment. In other words, the speech should be "partially protected" - if the police tell you to stop saying such and such in a particular situation, and you refuse to comply, then a charge of disorderly conduct may be in order, but if you do comply and go and say the same exact words in a different environment where a reasonable person wouldn't foresee that those hearing your words would react in a way that is criminal, the police shouldn't be allowed to touch you.
A hypothetical (I hope) example would be a person bent on inciting mischief (or even a person with no such motive but a huge lack of awareness of human behavior) going to a large, not-all-that-well-organized protest against the recent events in Ferguson, Missouri and saying quite loudly that "poor people should be allowed to walk into any store and take what they want" while not saying anything that sounds like "let's go raid the store across the street now" (that would be inciting others to commit a crime, which is likely already in the "not protected" category).
The police should rightly be able to order the person "cease and desist" as a reasonable person would view the words said in that specific context where the crowd is both large and not following a single leader as likely to incite at least one protester to commit a criminal act (note that this assumption that the words plus the situation would likely result in a criminal act likely wouldn't hold if the crowd was small or the number of people not respecting the protest's leader's instructions were small). If the same person then wrote those exact same words in a newspaper column or a blog, and took no specific actions to make sure that his words were seen by the protesters, then the police should leave him alone, he's just stating his opinion.
Now, we as a society have to be very careful about this. When in doubt, leave people alone to say what they want. If the end result is violence or other criminal acts, then the next time someone says something similar in a similar situation, the police will be able to rightly claim "history has taught us that if we don't get this person to pick a better time and place to speak his peace, criminal acts are likely to occur."
A similar situation exists with speech that is directly threatening:
* Does it actually cause someone to fear for their life or safety?
* Would a reasonable person see that the person's words, delivered in the manner in which they were delivered, cause a person to fear for their life or safety?
* Given the entire situation, is it crystal clear after the fact that there was a clear, actual, intentional, credible threat?
If the first two questions are yes and the 3rd is no, then the proper police response is to shut the guy down and tell him to find a different way of communicating the same message. Of course, if all 3 are true then that's already covered by existing statutes and case law.