After five weeks of nearly single-minded concentration on the plight of 50 Americans held hostage in Tehran, U.S. policymakers have been suddenly beset by a host of urgent problems elsewhere in a troubled world.

Within the past several days this country's extensive and varied world-power responsibilities have come to the fore in widely separated parts of the globe. Situations in Asia and Africa as well as Near East problems separate from Iran are suddenly near the top of the foreign policy agenda.

Yesterday's early-morning reports of a shootout at the residence of South Korea's martial-law commander, Gen. Chung Seung-Hwa, suggested new violence in the struggle for leadership of the strategic and militarily exposed U.S. ally.

As the day wore on, it appeared that a military group headed by the defense security commander, Gen. Chon Tu-wha, had deployed forces without civilian authority in an effort to bring down the martial-law commander, who is believed by many to have been implicated in the recent assassination of President Park Chung Hee. Eventually Chung and Several other generals were arrested for investigation in connection with the assassination.

The State Department, in an effort to forestall a coup, issued a warning to the military last night that any move to disrupt that country's democratic processes would have a "severe adverse impact" on U.S.-Korean relations.

Even before this unexpected jolt from Asia, senior officials had diverted some of their attention from Iran to neighboring Afghanistan, where newly arrived Soviet troops appear to signal a decision by Moscow to redouble its bet on the shaky regime of Hafizollah Amin.

Within the past several days, U.S. intelligence had picked up the movement of one or two Soviet battalions, organized and armed for combat, to the vicinity of the Afghan capital of Kabul. These 400 to 800 Soviet troops were an addition to 3,500 to 4,000 Soviet military personnel already in the country.

To protest the troop movement, Deputy Secretary of State Warren Christopher on Tuesday had called in the Soviet Union's acting ambassador, Vladillen M. Vasev. The State Department, in making public the intelligence and the protest yesterday, was careful not to describe the new force as "combat troops," although that term could easily be applied. The last thing the Carter administration needs is another "combat troops" hassle with Moscow, as in the recent Cuban episode.

Meanwhile, southern Africa claimed a share of attention by senior policy-makers. The British decision to take Rhodesia back under its colonial wing temporarily and to lift economic sanctions against that country posed an urgent Washington problem of how -- and how quickly -- to respond.

The State Department yesterday praised the British proposals for a cease-fire and transition to internationally accepted constitutional rule in Rhodesia, but had no announcement about lifting U.S. economic sanctions. Policy is caught in a cross fire of competing opinions at home and abroad, including differences of view among policymakers. State Department spokesman Tom Reston said there may be an announcement, presumably on the lifting of U.S. sanctions, "very shortly."

In addition to these three urgent problems, several situations elsewhere are claiming a share of attention from crisis-ridden American officialdom:

An emotional dispute with Japan, the United States' ally in Asia, over heavy purchases of Iranian oil and other economic nods to Tehran since the onset of the U.S.-Iran crisis. The flashpoint for the dispute was public criticism of Japan by Secretary of State Cyrus R. Vance in Europe early this week. The U.S. indignation quickly spread to Congress, where strong statements against the Japanese continued yesterday.

House Speaker Thomas P. (Tip) O'Neill (D-Mass.) said that if it were within his power, he "would teach them a lesson" about loyalty to the U.S. ally. GOP presidential hopeful John B. Connally, who is often bitterly critical of Japanese imports, called Tokyo's posture "typical" in the pursuit of Japanese national interest, but also said "we have to be understanding" of Japan's near-total dependency on imported energy.

In another sign of anger about Japan, all but four of the 36 members of the House Ways and Means Committee introduced legislation empowering the president to increase duties up to 50 percent on imports from countries that do not cooperate with U.S. policy on Iran. Diplomatic sources anticipate a response to all this from Japan within a day or two.

Relations with Saudi Arabia and other nations of the oil-rich Persian Gulf, which are of unusually pressing importance on the eve of the next meeting of the OPEC oil cartel Sunday in Caracas, Venezuela.

Administration officials went to Capitol Hill yesterday to defend a proposed $120 million munitions sale to Saudi Arabia before the House Foreigh Affairs Committee, where military sales to the Saudis have been contested in the past by friends of Israel. Undersecretary of State Lucy W. Benson said the impact of any decision by Congress to disapprove the sale would be "very grave." But there is no sign of strong opposition in the present circumstances of increased uncertainty and increased U.S. dependency in the Persian Gulf.

Famine and tension in Cambodia, which had captured the world's attention before events at the Embassy in Iran drove it out of the headlines

U.S. military sources said yesterday that another round of fighting between China and Vietnam is likely, with Cambodia the fulcrum of the conflict. This time, the sources said, there is a greater chance that fighting could spill over to Thailand, a U.S. ally.