A battle-scarred Alexander M. Haig Jr. returned to Washington early yesterday from his longest, most important and most controversial overseas trip as secretary of state -- a 16-day, 27,000-mile journey to China and back that took him from diplomatic heights in Asia to a political downer on the way home.

Speaking to reporters in the presence of President Reagan in Los Angeles Thursday, Haig pronounced his mission "as successful as it could be" in repairing and advancing U.S. ties across the Pacific. Many of the foreign diplomats he met in China, Southest Asia and New Zealand echoed this view both publicly and privately.

The difficulties, which at the end attracted more attention than the accomplishments, came from two directions:

First, growing expressions of doubt about the Reagan adminstration's overarching emphasis on arms buildups and anti-Sovietism, both of which were neatly symbolized in the decision to supply U.S. arms to the People's Republic of China. One of the reasons for the intensity of the reaction was the drama of the announcement, made by Haig in Peking at a time and place and in a fashion not of his design.

Second, continuing problems of articulation by Haig and his senior aides. The most serious gaffe was the misguided and self-damaging attempt by Haig's aides to depict him as the long-distance hero of the United Nations vote condemning Israel for its raid on Iraq, and to depict Ambassador Jeane Kirkpatrick as a fumbler.

Haig, as a result, emerged from a mostly successful trip more controversial than when he left. His reaction to renewed criticism over the Kirkpatrick flap on the final leg of the trip was to isolate himself and his aides from the press in a severe case of lockjaw which, if it continues, could intensify his problems.

The Kirkpatrick affair, to deal with the last first, was a product of a conscious decision to provide two reporters, from The New York Times and The Wall Street Journal, with details of Haig's on-the-road involvement in the decision on the U.N. vote in New York. Haig's press spokesman, Dean Fischer, and the State Department's chief of politico-military affairs, Richard Burt, invited the two reporters to a late-night "background" briefing last Monday at the Wellington, N.Z., hotel where Haig, his staff and the traveling press were staying.

What is known, because The Washington Post's reporter stumbled upon this bar-side briefing, is that Fischer came armed with a sheaf of notes. This and the fact that Fischer is an extraordinarily cautious spokesman suggest that he was acting with direction or at least authorization from on high.

It is not known whether the aides intended to criticize Kirkpatrick in the process of extolling Haig. But the Times account Wednesday morning focused on the criticism, provoking immediate and widespread outrage, not least from President Reagan, who is particularly proud of Kirkpatrick.

Haig by then was in Hawaii resting on his way home. After speaking by telephone both with the White House and with someone in France, where Kirkpatrick was on vacation, Haig appeared suddenly before reporters Wednesday afternoon to deny strongly any criticism of the U.N. ambassador.

"That's it," snapped Haig as he finished his one-minute statement and strode briskly out of the room. Those were his final words to the press corps on the trip. He avoided the reporters abroad his plane on the long journey from Honolulu to Los Angeles to Andrews Air Force Base, and his aides did likewise. The most substantive thing heard from any of them was "no comment."

The Post's White House correspondent, Lou Cannon, reported from Los Angeles yesterday that the Reagan high command seems inclined to let the matter drop. While the incident is considered "a needless controversy" that resurrected questions about Haig as a Reagan-style "team player," it is not likely to lead to action against Haig or his aides unless it is repeated, White House sources said.

The final two days in Honolulu were a rest stop for Haig, as were the first two days of the journey in Hong Kong, after the long flight west. During the trip itself, time was set aside for the secretary's recreation, especially the tennis games he craves.

All this was in contrast in Haig's initial overseas venture, a stupefying nine-nation, eight-day journey to the Middle East and Europe in early April. Haig had "run out of steam" by the time that trip was half over. He swore he wouldn't repeat that folly, but would pace himself on future trips to preserve his effectiveness.

Before the Kirkpatrick incident, Haig also was more accessible to reporters on the Far East trip than at any time since assuming office. He had on-the-record press conferences in Hong Kong, Peking, Manila and Wellington. The famous "senior official" who often speaks authoritatively for secretaries of state met reporters in "background" sessions in Hong Kong, aboard his airplane en route to Manila and in Wellington. And Haig customarily strolled down the aisle as his Air Force 707 got under way to banter with 13 reporters occupying the last of the 43 passenger seats.

Despite these efforts, Haig was not entirely successful as a communicator with the press. On several occasions he came armed with lengthy presentations, similar to military briefings, and seemed frustrated that reporters largely ignored them to focus on unfolding and often controversial developments.

Moreover, Haig found it difficult to deal seriously and substantively with journalistic questioning of his premises. Instead, he tended to grant the validity of the question, then restate his position as if he were reluctant to reveal more of himself or his thinking. Haig's tortuous use of language is well known, to the point that he often jokes about it. As he becomes more confident of his position -- if he does, in the light of recent events -- he may learn to deal more successfully with the press.

Shortly before Haig left Washington, a decision was made at the highest levels of the government to inform the Chinese leaders that the United States was ready to make them eligible to purchase American arms. Inauguration of the first Sino-American arms relationships if of great political and strategic significance, whatever the prospect of large scale military purchases. Thus it was understood in advance that the manner of its revelation was important.

A Reagan administration action to amend the muniutions list to make China eligible for U.S. weaponry would require public notice. But Haig was to inform Peking only of the U.S. intention to take that action, and therefore the subject could be kept quiet for the time being.

Before leaving for China, the "senior official" told a background briefing at the State Department that "there have been no decisions of any kind with respect to the provision of arms to the People's Prepublic of China." He did not reveal that a decision was in the making, in response to requests from China, to permit such a "provision of arms."

The U.S. plan as Haig arrived in Peking was to keep the arms decision quiet at least until he left China, and make it known in a briefing later, along with a large number of other items of Sino-American business. This would mute the drama and diminish the public impact.

But, confronted with a question on the subject in a press conference on his final night in Peking, Haig let the cat out of the bag, revealing that "munitions list restrictions will be removed in general [from China]." Followup questions established that the United States had agreed in principle to provide China with weapons. This was big news, and, in a manner of hours, had ricocheted around the world.

Haig spent a great deal of time during the rest of tour seeking to convince Asian diplomats, as well as the American press, that this was a bureaucratic decision of limited significance -- to change the munitions control "category" of China.

But there was no way to nullify the impact of the original press conference statement, and Haig's trip is likely to be remembered for the announcement of the arms relationship between Washington and Peking long after everything else, including the Kirkpatrick controversy, has been forgotten.