It's rare. Mostly they incite laughter and amusement, which is why there is so much police reality entertainment on TV. Your standard for tossing the First Amendment is disturbingly low, as low as the left's standard for tossing the Second. Unless Gates was making credible fists, swinging his cane, or yelling for the crowd to attack, his disorderly speech did not rise to the level of disorderly conduct. He has a case for false arrest, and it would be patriotic to pursue it to push back on government worker conduct. The police are held to a much higher standard while on the taxpayer clock.
The officer's training would instruct him to be wary of a gathering crowd. While you wouldn't expect a Cambridge gathering to be in full "kill the pigs" mindset, he's already got one guy who seems to be a little off the plumb of acceptable social behavior, maybe he's got like-minded friends.