The transatlantic shuttle diplomacy that has occupied Secretary of State Alexander M. Haig Jr. for two weeks has produced sideshows here that again have raised basic questions about the environment for foreign policy in the Reagan administration.

These sideshows involve a strange mix of events.

They include seemingly trivial squabbles over Haig's personality in the administration at a time when he is engaged in trying to solve a serious international dispute, leaks to the news media that are sometimes wrong and seem to undercut Haig's mission, and gaping holes in the State Department bureaucracy that are revealed when Haig is tied up.

Whatever the outcome of the dispute between Britain and Argentina over the Falkland Islands, the lesson that now seems clear is that official Washington can be its own worst enemy at trying to deal with matters of substance versus matters of personality.

Haig stands at the center of what is happening. He is the solution and, rightly or wrongly, part of the problem.

By virtually all accounts from U.S. specialists and foreign diplomats, Haig is the best the Reagan administration has to offer in the way of well-informed, experienced and respected foreign policy makers and implementers.

But the former four-star general also has an occasionally prickly personality and is, as one White House official puts it, "very perk conscious," meaning that he likes the trappings of power.

This kind of thing may not directly affect Haig's relations with the president, but it seems to be an undeniable irritant elsewhere in the White House.

Thus, at the start of Haig's shuttling around the Atlantic and as that shuttle continued, The New York Times carried three stories about Haig and an internal dispute with the White House over which plane the secretary should take on his journey.

The issue was whether Haig would fly in a windowless plane, which he did not want. Haig's aides say the issue was Haig wanting a plane with better communications. White House officials say it was the windows. Whatever is the case, the episode and the revelation of it by officials to the press helps to poison the atmosphere at the highest levels of government.

Similarly, that same atmosphere produces a measurable dose of cynicism among some administration officials about Haig's overall mission in the Atlantic. Is he motivated by finding a solution or by trying to leap into the same class of global statesmenship as his former boss, Henry A. Kissinger? Again, it is a question that is inevitable, given Haig's background, but one that seems to trivialize American foreign policy.

Amid his travels came news leaks that the United States was giving assistance to Britain and that Moscow was giving intelligence information to Argentina. Then came reports that the United States was also giving intelligence to Argentina. Then columnist Jack Anderson acquired the partial transcript of a telephone conversation between an airborne Haig and a vacationing President Reagan.

As best as can be determined, the reports of U.S. assistance to Britain are accurate, although this assistance is not as extensive as has been described in some accounts and is relatively normal, given the mutual military arrangements between the two allies.

Reports about the Soviets having given intelligence to Argentina are not true, senior officials say, though the Soviets clearly are gathering data on the British fleet. The reports about the United States giving intelligence data to Argentina also are not true, officials here say.

Nevertheless, all these reports were potentially damaging to the effort to mediate, and none came out of thin air. Somebody told reporters about these developments or confirmed things that either were not true or that officials "assumed" were true but really had no evidence to support. Here, too, there is cause for wonder about the motives behind some of these leaks.

Haig's travels in search of a Falklands solution have also raised questions publicly about the wisdom of focusing so exclusively for so long on one issue while the Middle East, Central America, Poland and a dozen other potential flash points simmer. Some ask if this kind of sudden and intense attention does not somehow reflect an administration tendency for brief bursts of energy on an issue without really resolving it.

Supporters of Haig, and even those sometimes critical of his style, do not buy this argument. They say nothing elsewhere seems immediately explosive enough to demand that Haig end his efforts on the Falklands.

Indeed, while the Falklands crisis started with a comic-opera quality, it is a deadly serious business in which lives could be lost, two governments could fall, and the Royal Navy, the best and biggest allied fleet in Europe, could be tied up indefinitely more than 8,000 miles from where it is supposed to play a key role in the North Atlantic alliance.

What the situation does cast a spotlight on, however, are the continuing vacancies in the State Department bureaucracy.

In Haig's absence, the deputy secretary of state, Walter J. Stoessel, had to be sent to the Middle East to ease tensions there even though Stoessel is not a specialist in that region. Lawrence S. Eagleburger, State's energetic, all-purpose No. 3, is running the department's daily operations.

Eagleburger was formerly in charge of European affairs, but nobody has been named to replace him, and Haig's choice, Richard R. Burt, the current director of politico-military affairs, is said to be opposed elsewhere in the administration.

The job of counselor of the State Department--a key post vital to the smooth working of State that had been filled by the highly regarded Robert C. McFarlane, who now works for the White House--also is still vacant.

Another key post, undersecretary for economic affairs, has been vacant for many months since Myer Rashish was let go by Haig, who is also encountering opposition in the White House to his preferred choice for that job.

"In this administration," says one frustrated friend of Haig's, "everything is personalities, everything."