THE BRIEF BUT UGLY outbreaks of street fighting here during the visit by the Shah of Iran leave a number of reputations suffering severe bruises. The American authorities lost control of a crowd that was clearly spoiling for a fight. The Shah's government, behaving - logically enough - like an authoritarian monarchy, contributed to the provocation with its paid demonstrators. As for the young Iranian students with their chanting and their baseball bats, they seem to have left town thinking that they scored a triumph by disrupting the visit. In fact, they have a good many Americans under the firm impression that this alternative is hardly any more appealing than the present Iranian regime.

When a foreign visit ends with a flood of casualties to hospital emergency rooms, it's obvious that the hosts mismanaged the affair. Appraently the Carter administration was leaning over backward to avoid any resemblance to the methods of the Nixon years. The result was to leave an inadequate contingent of Park Police, not even wearing helmets, facing the crowd as it prepared to rush them. For reasons still not clear, the federal authorities never called in the Metropolitan Police.

That was a serious mistake. The Metropolitan Police have had far more experience with crowds than any of the federal forces, and some of the Metropolitan units are trained for precisely this work. They have repeatedly shown that the surest way to avoid bloodshed is to impose a superior force from the beginning. The present tenant of the White House, to his credit, dislikes displays of force. But he would be exceedingly unwise to let Washington become known as city where it is cheap and easy to disrupt public events and assault policemen.

The people chanting "Down with the Shah" were protesting the repression of human rights in Iran. Americans have a responsibility not to ignore that repression. But if the Shah's record in this respect is not the best in the world, neither is it the worst. "We can nourish no illusions that a call to the banner of human rights will bring sudden transformations in authoritarian societies," Secretary of State Cryus Vance said last April. "We are embarked on a long journey."

Mr. Vance also observed that one of the surest ways for Americans to advance the cause of human rights abroad is to preserve and enhance them in this country. Measured by that standard, the past couple of days were not a success. Freedom of expression does not include the freedom to beat up the people who disagree. The First Amendment provides no right to throw bottles at policemen. Rights survive and flourish only in an atmosphere of civil peace. A riot on the Ellipse is not likely to persuade the Shah to relax police controls in Teheran.