The failure of the Moscow talks on strategic armaments - and the sense of near-crisis that resulted - dramatically illustrate the dangers of President Carter's unorthodox methods of public diplomacy.

Having created high expectations and a high-profile position by unveiling the essence of his strategic arms limitation proposals in advance, Carter is faced with severe political and policy problems following Russian rejection of the proposals.

The Soviet leaders' attitude was hardly a surprise, given the long history of their negotiating position and their statements in response to Carter's in recent weeks. What was more of a surprise - and what has dismayed Carter administration officials as well as diplomatic observers - is the worldwide wave of apprenhension arising from the Moscow events.

Soviet Foreign Minister Andrei Gromyko's public denunciation of the U.S. proposal in a highly unusual Moscow press conference yesterday adds another dimension of gloom and a further suggestion of crisis. Gromyko appeared to be reacting to Carter's well-publicized determination on Wednesday to "hang tough" behind U.S. proposals he declared are "fair" and "balanced."

U.S. official spokesmen here sought to defuse public concern. White House press secretary Jody Powell, while giving no hint of a softening of the U.S. position, emphasized that "it is important to be patient, to be methodical" and said Carter intends to be so Defense Secretary Harold Brown, through a spokesman, said he has no intention of speeding up development of the cruise missile, B-1 bomber, MX missile or any other weapon in response to the Moscow events.

From the beginning of his campaign for the presidency, Carter attacked secret diplomacy as practised by then Secretary of State Henry A. Kissinger and others in recent administrations, declaring that all major mistakes of U.S. foreign policy flowed from a closed-door process of decision - making. "We must never again keep secret the evolution of our foreign policy from Congress and the American people. They should never again be misled about out options, our commitments, our progress or out failures," he declared in his first foreign policy statement, issued while he was in Tokyo for a Trilateral Commission meeting in May, 1975.

Once in office, Carter made impromptu public declarations about foreign policy matters the centerpiece of his diplomatic method. This has been popular at home so long as the statements expressed widespread attitudes and seemed to give hope that the United States could get its way. But in several cases the method has brought serious complications.

Carter's statements outlining his ideas of a Middle East peace surprised his own diplomatic advisers and jolted Arab and Israeli leaders alike. Israeli Prime Minister Yitzhak Rabin, in the midst of a fight for his political life at home, was in the awkward position of having conferred at length with Carter just before presidential statements that were at odds with Israel's official positions. The Arabs, like the Israelis, were delighted by some Carter sentences and phrases and dismayed by others.

"Going public" with his Middle East views at this stage could help shake loose fixed positions if all goes well. But it could lead to dangerous acrimony, this time directly involving the U.S. President, if the parties refuse to compromise.

The public aspects of Carter's much discussed human rights diplomacy have brought sharp reactions from goverments that were critized. Five Latin American governments have renounced U.S. military aid because of Carter administration actions and statements, leading Secretary of State Cyrus R. Vance to suggest that congressionally mandated human rights reports might more usefully be confidential. Carter's strong remarks about "horrible murders" in President Idi Amin's Uganda were applauded by most Americans - until they led to a threat to U.S. citizens in Uganda.

To some degree Carter's outspokenness is a natural swing of the pendulum from Kissinger's highly secretive methods, the full extent of which is still coming to light. It was revealed this week, for example, that the United States held secret talks with Cuba for 12 months in 1974-75 known only to Kissinger and his two negotiators - and kept secret even from the State Department country director charged with monitoring and coordinating U.S. policy toward Cuba.

Kissinger's methods generated waves of antipathy in Congress and the bureaucracy and among segments of the public. It probably would have been impossible for such secretiveness to continue, even had Kissinger remained in office.

While strongly critical of secret diplomacy, Carter and his team are now beginning to experience the severe problems of public diplomacy - inflexible positions, international bad blood, open confrontations flowing from open declarations.

These dangers are heightened in the age of worldwide and instant communications, when the press conference of a President or a Soviet foreign minister can be transmitted around the world with powerful velocity and potential impact to match.

A self-centered America convinced that its positions of the moment are moral and right, led by a President who is telling it so, could blunder into unnecessary and even sinsoluble difficulties with other nations having priorities, interests and convictions of their own that they see as equally legitimate. This is particularly so at a time when U.S. power relative to other nations is seen to be declining.

The great question is whether Carter can somehow learn to preserve the advantages of public support and open diplomacy while moderating the extremes and reducing the dangers. That question is unanswered now, while the returns are still arriving from Vance's Moscow mission.