The leaders of Third World countries participating today in the United Nations' 40th birthday ceremonies pointed to the superpower arms race as the most dangerous problem facing the world and urged Washington and Moscow to take tangible steps toward arms control at their summit meeting next month.

But if the rhetoric concerned the agenda of international politics, much of the reality of the day was taken up with diplomatic and security headaches brought on by the gathering of about 60 world leaders at U.N. headquarters for the week-long celebration.

President Mauno Koivisto of Finland arrived at the U.N. complex today half an hour before an appointment listed on the protocol department's schedule, on foot rather than in a motorcade. He entered alone and without ceremony, flashing his pass at the public gate.

Yesterday, the week's first speaker, Nicaraguan President Daniel Ortega, got lost in the U.N. corridors after his meeting with Secretary General Javier Perez de Cuellar, and proceedings were delayed half an hour before he found the right entrance to the assembly hall.

Security was so tight for Indian Prime Minister Rajiv Gandhi, because of threats against his life by Sikh militants in New York, that U.N. gates were closed to all vehicles when he entered the building today to preside over a meeting of the Nonaligned Movement. This briefly blocked the motorcade carrying Ortega to the same meeting, and left it on the street outside with sirens wailing.

Some VIPs found no need to pull rank. As Swedish Prime Minister Olof Palme sat in his chair in the assembly chamber, the seat behind him, usually the province of junior diplomats carrying schedules and speech texts, quietly was occupied by Carl XVI Gustav, the king of Sweden.

At today's General Assembly session, one of the most specific suggestions by the 20 speakers was made by Ranasinghe Premadasa, Sri Lanka's prime minister, who said the General Assembly should adopt a "special emergency resolution" appealing to President Reagan and Soviet leader Mikhail Gorbachev to cut military expenditures by 10 percent for the next five years.

A significant portion of this money, which he calculated at $60 billion a year, should be allocated to cut the international debt of the poorer nations, he said.

"What we seek is not merely debt relief, but an investment to safeguard and improve life," Premadasa told the assembly. "What we demand is an end to a system where the security of many is hostage to the ambitions of a few."

Zambian President Kenneth Kaunda, welcoming the Geneva meeting of Reagan and Gorbachev, commented: "May I humbly remind them that the international community is more interested in substance than in rhetoric and mere posturings."

Angolan President Jose Eduardo dos Santos also called the danger of a third world war the major concern of all nations.