The General Assembly opened its 37th annual session yesterday at a time when the United Nations is being widely criticized for failing to deal effectively with the political issues clogging its 137-item agenda.

In his annual report to the Assembly, Secretary General Javier Perez de Cuellar conceded that the world body is failing in its task of keeping the peace and serving as a mechanism for settling international disputes, special correspondent Michael J. Berlin reported.

Many of the about 70 foreign ministers who will address the assembly in its opening weeks are expected to touch on the question of reinvigorating the United Nations. But for most, their real purpose in flocking to New York is the round of bilateral meetings, which often achieve more meaningful results.

It will be the first General Assembly for Secretary of State George P. Shultz, who is scheduled to meet with his Soviet counterpart, Andrei Gromyko, Sept. 28.

The major business transacted yesterday was the unopposed election of Hungarian Deputy Foreign Minister Imre Hollai as assembly president.

Among the new items on the agenda is a Cuban attempt to hold a full-scale debate on the status of Puerto Rico. The United States opposes any debate, contending that Puerto Rico is a self-governing commonwealth, and therefore not a proper subject for U.N. debate.