In four months as secretary of state, George P. Shultz has won uniformly high marks throughout the Reagan administration as a calm problem-solver.

"A 100-watt bulb that is on all the time," as one official put it, "in comparison to the firefly that was Al Haig."

Shultz played the key role in helping reshape administration policy in the Middle East and has skillfully helped the administration put behind it a destructive quarrel with European allies over the Soviet natural gas pipeline.

If former secretary Alexander M. Haig Jr. had tried to do that, one official said, "it would have been greeted with major suspicion" in the White House and Pentagon, "because Haig was viewed as a mouthpiece for the Europeans."

Shultz, he said, has the same views as Haig but can pull off such a switch because his style of operation is so different and so much more broadly acceptable in the White House than his predecessor's.

Trade and the Middle East are two areas in which Shultz, a former Treasury secretary and president of a company with extensive dealings in the Arab world, has a lot of experience.

But there are other crucial policy areas--Central America, relations with China and arms control with the Soviet Union--in which the secretary has not yet made his views or his presence felt, officials also said.

This is primarily because the Middle East has occupied so much of his time. Indeed, as Shultz said during a recent breakfast meeting with editors and reporters of The Washington Post, "I think unless you do something about it, in the job of secretary of state you will spend 100 percent of your time on the Middle East. The subject consumes you and it's coming at you all the time."

Shultz' way to cope and to learn about the other problems is to convene private seminars in his office, bringing in experts from inside and outside the government to talk over problems and potential ways to solve them.

He has done this on the Middle East and the Soviet Union. A session on South America was scheduled yesterday, and one is scheduled in early January before his trip to China.

It is in the area of nuclear arms control, however, that a lack of involvement by the secretary is potentially most serious, according to a number of senior State Department officials.

The secretary, these officials said, is not particularly well educated at this point in the arcane matters of nuclear weapons and negotiations on how to limit them.

He is viewed as not likely ever to be as involved as Haig, a former four-star general who, while a certified hawk on defense, was nevertheless an important force pressing for arms control as a part of overall United States and western alliance policy.

Officials who tend to favor arms control, including some at high levels, expressed concern that, without Shultz' full involvement, experts at lower levels in the Pentagon and elsewhere may be able to exercise a de facto veto of arms-control efforts simply because of their greater involvement and knowledge.

These officials said they do not know whether Shultz is inclined to become a strong advocate of arms control.

But they said a key problem is that ideas on the subject tend to enter the administration's thought process from the bottom rather than from the top levels.

Shultz, because of the esteem in which he is held, would be an important influence on President Reagan at the top, the officials said.

Some of Reagan's top aides insist that the president is a strong supporter of arms control and intends to pursue it.

But the problem, officials said, is getting Reagan and other top policy-makers to focus on the important details of this subject -- such as what to do about thousands of newly planned cruise missiles -- if any real progress is to be made.

Time is important, these officials believe, because arms talks in Geneva with Moscow are under way and new deployments of weapons on both sides are drawing near.

The question, according to one official, is not only whether the secretary will involve himself but "will it happen in time."

When asked about these concerns and his involvement in arms control, Shultz said:

"I've spent a lot of time on the subject. It's a subject I followed as a reasonably interested newspaper reader before, but I've never worked at it. So relative to some other things, it's a new issue to me.

"It's an issue that has tremendous complexity to it in one sense. In another sense, it is beautifully simple in its broadest dimensions.

"I don't feel awed by it," he said, "as though somehow it's beyond understanding. So I'm working on it quite hard . . . fighting for time on subjects like arms control . . . and trying to get a sense of the relationships among the various parts of the subject."