Legal Definition: "The unsettling of proper order by creating loud noise by fighting or conducting other unsocial behavior that upsets people. Punishable by either a fine or brief term in jail, disturbing the peace is considered a misdemeanor"
As the Henry Louis Gates Jr case has demonstrated, a charge of "disturbing the peace," is the modern day nightstick used by police to maintain their authority over anyone who challenges or criticises them. Fifty years ago, verbally challenging or berating a beat-cop might prompt the officer to pull out his nightstick and slap it in his hand while he told you to "watch your mouth." If you gave him more "lip" you would get a rap on the head or knuckles. Today you are threatened with a charge of disturbing the peace--even if you are standing on your own porch. The law is vague enough that the officer can always reasonably justify the arrest and a good attorney can get the charges dropped. That's fine with the officer, the arrest served its purpose: knuckles were rapped, power was demonstrated and deterrent maintained.
Now every police officer should be respected because of their position. They represent the law, and disrespecting an officer is showing contempt for the law which is the framework that holds up any civil society. But showing respect is a matter of good citizenship and good manners, rarely is it a legal requirement. The purpose of the law is to protect its citizens from the abuse of power -- whether that power is in a gun, a bribe, or the power of the police to arrest. The purpose of law enforcement it to encourage, even coerce, obedience to the law. It is not the purpose of law enforcement to coerce good citizenship and manners.
Where then is the line? It is in the law. Were the loud complaints and accusations that Mr. Gates made from his porch a clear breach of the law? No. Were his actions a "threat" to the the peace of the community? No. Once the police established his identity as the resident of the home, they had no further business on the property and should have departed, ignoring Mr. Gates complaints. If Mr. Gates chased them down the street, then a charge of disturbing the peace would have been appropriate.
Loudly accusing a police officer of racism is not a crime. The officer should have remembered the children's chant: "sticks and stones may break my bones but words will never hurt me." Arresting Mr. Gates was a clear abuse of police power.