The air here is filled with a mixture of gloom and hope as the 38th General Assembly of the United Nations gets under way. Gloom because many delegates fear that the Soviet-American shouting match, exacerbated by the shooting down of Korean Air Lines Flight 7 on Sept. 1, will reverberate through all the debates and stymie the General Assembly's work.
Hope because, for the first time since 1960, three dozen chiefs of state and of government will come to New York and speak out for moderation, for conciliation, and for strengthening the role of the UN.
''The US intends to rub the USSR's nose in its dirt,'' said an Asian diplomat who is known to be a conservative.
President Reagan, who is scheduled to address the General Assembly on Sept. 26, will ''exploit the Soviet blunder to its fullest extent for domestic as well as foreign political purposes. The Soviets will respond in kind, and both superpowers will show little patience for those who may resist lining up with one or the other,'' the diplomat predicted.
Some of the Reagan administration's thunder, however, has been stolen by the decision of the governors of New York and New Jersey to bar Soviet Foreign Minister Andrei Gromyko's plane from landing at Kennedy or Newark airports. Gromyko's absence - he rejected Washington's offer of a military airport - reduces the target for Western ire over the jetliner incident.
And Monday's angry remarks by American delegate to the UN Charles M. Lichenstein - that if member states felt they were unwelcome they should ''seriously consider removing themselves and this organization from the soil of the United States'' - also are seen by Western diplomats here as weakening their tacit joint strategy of using the UN to score points off the Soviets.
Many diplomats here expect the US-Soviet tussle will leave frozen issues such as Afghanistan, Namibia, the Falkland Islands, Kampuchea, the Western Sahara, disarmament, and the North-South dialogue on economics, since there is little or no political give on either side of these various issues.
But the atmosphere may improve on Sept. 27 and 28, when three dozen heads of state and government - Western, communist, and nonaligned - convene in New York to address the General Assembly and hold two informal meetings. Reliable sources say the meetings will center on disarmament and security development, economic problems affecting North-South relations, and the need to strengthen the UN.
''This mini-summit is expected to function like a think-tank, a kind of follow-up on the Cancun (the 1981 North-South summit),'' a diplomat says.
France's President Francois Mitterrand, Sweden's Olof Palme, Canada's Pierre Trudeau, Morocco's Hassan II, Egypt's Hosni Mubarak, as well as the presidents or prime ministers of Colombia, Tanzania, Yugoslavia, Ethiopia, Austria, Finland , Poland, and Hungary are expected to participate in two summit meetings, with UN Secretary-General Javier Perez de Cuellar sitting in.
''In 1960, Nasser, Nkrumah, Nehru, Castro, Macmillan, Khrushchev, Sukarno came to the UN,'' says a high-ranking West European official. ''The cold war was then coming to an end.
''Now, another, perhaps fiercer cold war, since it is involving the entire planet, seems to be getting on its way. The UN summit meeting therefore is extremely timely. Mitterrand, Gandhi, Trudeau, and other respected voices will speak out for reason, for lessening international tensions, for dialogue, and for fresh thinking on key international questions.''
Considerable interest at the UN is raised in the emergence of two new items this fall.
* One concerns the fate of Antarctica, the huge, frozen, mineral-rich continent, larger than the United States and China combined. Will it continue to be governed by the 14 members of an exclusive club that signed the 1959 Antarctica Treaty, or will it be considered, like the sea, as ''the common heritage of humanity?'' Malaysia is pushing for a study and debate of the matter , but at this point both the members of the club and their opponents are moving cautiously.
* Another issue is a Soviet proposal to ban the use of force in outer space. The US may find itself isolated on this matter, since almost all UN member states, including those that generally side with the US and have no love for the Soviet Union, are strongly in favor of the demilitarization of outer space.
As for the UN itself, many observers seem skeptical about its role in the future. ''If the UN becomes merely a forum for propaganda wars and has its hands tied by the superpowers, it may soon go the way of the League of Nations,'' says an American diplomat who now watches the UN from a distance.
''This General Assembly way well break or make the UN and show whether it is still relevant to world peace and security,'' says a UN official who does not conceal his pessimism.