What Predident Carter said about Russia in South Carolina Thursday applies around the world. In dealing with the Mideast, the Allies and even Africa - as in dealing with Russia - no quick fixes are available.

So it is fine for the President to warn against overprojecting the "mook of the moment . . . whether euphoric or grim." It would be even finer if he practiced what he preached, if he conducted himself in a way that gave quiet professional diplomacy scope for a long haul.

The past week has been particularly rich in evidence of the arduous road ahead in international matters. The President, in his South Carolina speech, tried to patch up things with the Russians by assuring Moscow his humanrights campaign was not aimed at the Soviet Union, and by asserting that his arms-control proposals were an extension of the guidelines worked out at the 1975 Vladivostok summit meeting. He avoided grating terms such as "aggressive" and he ended the speech with an especially graceful quotation from Soviet leader Leonid Brezhev.

Even as Carter spoke, however, he reiterated views that have annoyed the Russians. He made the case for human rights anew, and said that Soviet-American relations were of diminishing importance in the world at large. He warned that this country would continue to develop its new cruise missile so long as Russia built up its force of heavy strategic weapons. Clearly, the gap between the two countries on arms control remains very broad.

The day before the South Carolina speech, Israeli Prime Minister Menachem Begin, during his visit, showed what a thorny negotiating path lay ahead in the Mideast. He accepted Carter's proposal for reconvening the Geneva conference and even one-upped the President by giving a date - Oct. 10.

But he asserted substantive positions far distant from the American view - and the Arab insistence - that the Palestinians beincluded in the conference. It will be very difficult for Secretary of State Cyrus Vance, on his coming trip to the Mideast, to persuade the Arab states to come to Geneva, and even more difficult to bring the parties together after that.

While Begin was in town Newsweek magazine appeared with charges by French President Valery Giscard d'Estaing that Carter's human-rights drive jeopardized detente with Russia. West German Chancellor Helmut Schmidt, who had made similar charges previously, did not air them publicly during his visit to Washington a fortnight ago. But he did make them privately. Moreover, in return for piping down in public, he got Washington to come off its insistence that he expand the German economy more vapidly and curtail his nuclear-power deal with Brazil. Despite the apparent harmony of the London summit, allied relations still have to be knit together.

Finally, there is Africa, where the administration has applied strong, public pressure for concessions toward majority rule by the white supremacy states of Rhodesia and South Africa. Last week Prime Minister Ian Smith of Rhodesia called for new elections - a sign that he was not yielding to the American pressure. Which means that further effort are required to foster a peaceful resolution of racial conflicts in southern Africa.

Carter has in the administration high officials eminently capable of dealing with these vexing problems. The staff of the National Security Council includes some excellent people. Vance, Secretary of Defense Harold Brown and the officials around them combine candlepower. If given a chance they can required for a fair degree of success in all the thorny areas.

But they can only get a chance if Carter lays off the pace a little - if he stops making public statements that suddenly raise issues that are embarrassing to foreign leaders. So the way toward a slow, steady traverse of the difficulties ahead in foreign policy is for the President to take his distances. He can do that easily by concentrating more on domestic problems- notably the problem of the cities to which he has so far paid not nearly enough heed.