The cop did not violate the law when he arrested Professor Gates. Professor Gates was injuring the Officer's pride, so the Officer lured him outside where his, well, rants, would be a punishable offense. The cop tricked the citizen.
As I wrote before, "disorderly conduct" must be done in a public place, or where the public could become alarmed. Now, on the face of it, there is no chance any of would be disturbed to the degree that we'd be inclined to call the police if we were to hear Professor Gates yell. The cop, however, knew that wasn't important.
Professor Gates was wrong to lose his composure, and not to insult the (almost certainly at least a little, aren't we all?) racist police officer with a raised voice, but to call him "Boy," "Stooge," or even "Fascist," in a calm cool voice, as if he ran the plantation, as if the Police Officer were his servant, a servant of the public, the public of which Professor Gates is a member. If the cop acted in a racist way (and we'll never know quite for sure), then that may well have been within reason.
But by raising his voice, Professor Gates opened up a possibility. In your home you can call a police officer anything you want, and act in any "tumultous" way you desire, and talk about the Officer's family, too. But on the street, you can't yell like that.
So, ask yourselves, why did the officer ask Gates out of his home if not to entrap him? Certainly he had broken no law so far. Why did Gates act so immaturely and yell, instead of with dignity and disdain, if one poor slob didn't treat him with the respect he felt he deserved?