The General Assembly's second special session on disarmament opened today with the two top United Nations officials frankly reminding the delegates that nothing concrete emerged from the organization's first such session in 1978.

"Not a single weapon has been destroyed over the past four years," Assembly President Ismay Kittani of Iraq said yesterday of the results of the earlier disarmament session. He called it "a sorry record of failure."

U.N. Secretary General Javier Perez de Cuellar recalled that the comprehensive program of disarmament adopted by the assembly in 1978 "has largely remained a dead letter." The goals in that program, he said, are "further from our reach now than they were four years ago."

It was on that note that the General Assembly began what will be five weeks of speeches on the need to end the arms race. At least 14 world leaders and high officials of 85 other nations are expected to talk. Among them will be President Reagan, Prime Minister Margaret Thatcher of Britain and West German Chancellor Helmut Schmidt. The Soviet position will be given by Foreign Minister Andrei Gromyko.

In addition, there will be briefer presentations from more than 75 representatives of nongovernmental organizations, including peace and arms research groups from around the world.

The outcome of all this talk is expected to be a new version of the disarmament plan passed four years ago. Despite this emphasis on action by the United Nations, however, there is recognition among some of the delegates that the international organization can do little more than apply moral pressure to its members that are actually in the arms race.

Kittani noted that when it comes to reductions in nuclear weapons, for example, the "superpowers," the United States and Soviet Union, "must lead the way if there is to be progress." Kittani welcomed the participation of world leaders but added that he hoped they "would not defend old, sterile and even dangerous positions."

Although he voiced despair at past inability to control the building of arms, the assembly president said there are two new factors today: "Economics are working in favor of rationality in the arms race," he said, referring to the high cost being borne by both superpowers in the building of new weapons.

He described as the "most encouraging" new factor "the growing and increasingly assertive public movements against the arms race."

Saturday an estimated 500,000 people are expected to march by the U.N. headquarters building and then gather in Central Park for a day-long antinuclear rally. A demonstration today near the United Nations drew a much smaller number. At mid-afternoon, only about 150 people were to be found.

Although the United States does not expect any direct pressure on it as a result of the General Assembly session, it has taken steps to meet what it sees as attempts to put the Reagan administration disarmament policy in a bad light.

By withholding visas from peace activists around the world--who, the administration said, were associated with Soviet front groups such as the World Peace Council--the State Department hoped to prevent speeches at public meetings here and in other American cities. That move backfired somewhat when it became apparent that among those barred from the United States were some who had actually been invited by the United Nations. The Justice Department announced today that it decided to waive the denials in 42 cases where the applicants had received personal invitations from the United Nations. The remaining 315 would continue to be denied visas, a spokesman said.

World Peace Council President Romesch Chandra of India, for example, said yesterday his visa forbids him from speaking at any gathering outside the United Nations.

Soviet journalist Gennady Gerasimov of Novosti, an official Soviet press service, was held up from participating in a U.N.-sponsored journalist meeting last week. He finally arrived today with a visa that limits his activities to coverage of the disarmament session. A year ago, Gerasimov said, pointing to his passport, he was given an unlimited visa to cover the General Assembly session.

Under terms of both visas, neither man is permitted to travel more than 25 miles from Columbus Circle in midtown Manhattan.

The U.S. delegation also may have problems with two resolutions expected to be introduced. One from India would say that any nation that uses nuclear weapons will be committing a crime against humanity. The Soviet Union may introduce a resolution calling for nations to agree to "no first use" of nuclear weapons. In the past the United States has opposed such resolutions.

To present its side of the issue, the U.S. delegation has opened an exhibit at its mission's headquarters. It features videotapes of Reagan's disarmament speeches and charts that show Soviet spending on arms as far greater than that of the United States.