January 1, 1981

The Algerian intermediaries in the hostage crisis flew home today to discuss with their leaders the latest American proposal before going on to Iran for what could be a decisive round of talks. With three weeks remaining in office, Carter Administration officials again contended that an American reformulation of previous proposals offered Iran a practical way to resolve the 14-month-old crisis if there was political will to do so. Meanwhile, the Iranian radio, in an unattributed commentary, broadcast a new threat to put the hostages on trial and possibly execute them. ''It is natural that according to Islamic laws, the trial of the hostages not only might lead to their execution, being guilty of spying, but even more important, it will expose the unwarranted interference of imperialism in other countries,'' the broadcast said.

The development of a promising screening test for carriers of cystic fibrosis, the most common lethal inherited disease of white Americans, was reported yesterday by medical scientists in Boston. Children born with the condition have trouble clearing mucus from their airways, become prey to infections of the respiratory tract and often die in their late teens or early 20's, although in rare instances they survive much longer. It is estimated that one in every 1,600 to 2,500 babies born alive in the United States is afflicted with cystic fibrosis. The disease is rare in racial groups other than whites. Sickle cell anemia, which affects blacks almost entirely, is 4.5 times more prevalent among blacks than cystic fibrosis is among whites, according to the Merck Manual.

After the most tortured census in American history, plagued by bitter lawsuits, the Census Bureau officially certified the 1980 population count of the states today and reported it to President Carter only hours before the legal deadline. It was able to do so only after the Supreme Court last night overturned an order by a lower Federal court that had blocked the certification, pending the Government's appeal of a successful assertion by New York City that its count should be adjusted to make up for New Yorkers overlooked by census takers. The final national population count, released today at ceremonies at the Commerce Department, of which the Census Bureau is a part, was 226,504,825. This was 11.4 percent above the 1970 count of 203,302,031 and somewhat higher than ''preliminary'' figures released earlier this month.

Corruption in state and local government in Massachusetts was so pervasive in the 1960's and 1970's that it became ''a way of life,'' a special state investigating commission concluded today after two and a half years of study. In one of the most sweeping indictments ever made of the conduct of a state government, the commission said that bribery, extortion, tax evasion, illegal campaign contributions and the laundering of money to disguise its origins were commonplace and that ''there is a tacit understanding between public servants and private professionals that this is how business is done in Massachusetts.'' The Special Commission Concerning State and County Buildings, set up in 1978 after the state's worst corruption scandal, said in its 2,500-page report that blame could not be narrowed down to a handful of individuals. 'Broad and Pervasive Pattern' ''It was not a matter of a few crooks, some bad apples which spoil the lot,'' the commission said. ''The pattern is too broad and pervasive for that easy excuse. At those crucial points where money and power came together, the system has been rotten.''

The Government index designed to forecast future economic trends rose significantly in November, the Commerce Department reported today, indicating that the weakness forecast by many economists is still not in sight. The 1.2 percent increase in the index of leading indicators - the sixth consecutive monthly rise - was viewed as confirmation that the economy was continuing to perform more strongly than the analysts expected. Although Government and private economists said that they still expected a weakening early in 1981, the addition of this latest statistic to a variety of similarly encouraging figures released in recent days made them less certain of their forecasts. Wonder 'About the Odds' ''It does make you wonder a little more about the odds we put on a decline in activity in the first quarter of next year,'' said Albert H. Cox Jr., president of Merrill Lynch Economics.