December 31, 1982

Governor Carey leaves office today, his record a mix of impressive success and puzzling lapses and his place in New York State's history still uncertain. As he has through most of his eight years in office, Hugh L. Carey still stirs strong passion. Admirers talk in heroic terms about the ''crisis manager'' who saved New York City from bankruptcy and led the state in a difficult new era of austerity and retrenchment. Detractors remember the brooding and inaccessible loner who had trouble maintaining ties with friends, subordinates or legislators. Assesments of his administration, gathered from a spectrum of experts both within and outside of the state government, are mixed, and not particulalry along partisan lines.

Two years ago in the sprawling black township of Soweto in South Africa, Representative Stephen J. Solarz, Democrat of Brooklyn, met an African employee of the United States Consulate in Johannesburg named Thabo Moeti. Mr. Moeti asked Mr. Solarz, who was chairman of the House Foreign Affairs Subcommittee on Africa, whether there was some way the American Government could help black South Africans receive university educations in the United States. There was. Mr. Solarz sponsored legislation that provided $8 million over two years for the black students to attend American universities. The first students to benefit from the legislation arrived in the United States for the current academic year.

In a year that produced the strongest sustained stock market rally in a half century and a new high for the Dow Jones industrial average, the biggest percentage gainers were typically small, obscure issues. To be sure, such household names as International Business Machines, General Electric, Procter & Gamble and American Express forged ahead. But none of these or the other 26 stocks in the Dow Jones industrials rank among the Big Board issues showing the largest percentage gains for this year, as calculated through Dec. 27. Some former Cinderella stocks performed beautifully, while others -notably energy issues - went into a tailspin.

President Reagan announced today that the United States would not pay a United Nations assessment of as much as $1 million a year. This is the first time, American legal experts said, that Washington has claimed the right to withhold funds. The disputed funds are Washington's share of the costs of a commission set up under the Law of the Sea Treaty that will design rules to govern the mining of minerals from the deep seas. Mr. Reagan refused to sign the treaty codifying law for the sea because of the mining provisions. In a statement issued from Palm Springs, Calif., Mr. Reagan said the funds ''are destined to finance the very aspects of the Law of the Sea Treaty that are unacceptable to the U.S.'' Moreover, he said, the assessment is ''improper'' and ''not legally binding'' because the rule-making commission is ''distinct from the U.N.'' Challenge to U.N. Seen The United States is now required to pay 25 percent of the United Nations' costs. Western diplomats here said Mr. Reagan's decision poses a fundamental challenge to the United Nations existence and compared it to the refusal by the Soviet Union and France to pay their share for peacekeepers in the Congo in 1960, the year the Belgian colony became independent.

The Government's index of leading economic indicators rose eight-tenths of 1 percent in November, the Commerce Department reported today. The index, which is intended to predict the future direction of the economy, has risen in seven of the last eight months, which ordinarily would signal that an economic recovery was under way. But at the present time, there are no sure signs that the recession has ended. In fact, a companion index of coincident indicators, which measures the current condition of the economy, declined six-tenths of 1 percent in November, the 14th consecutive drop and a sign the recession is continuing.