What was going on when I was born?

The National Highway Traffic Safety Administration today announced a preliminary finding that the brakes on 320,000 General Motor's 1980 X-model cars were defective. The agency scheduled a hearing for Feb. 14 on whether the cars should be recalled and the brakes repaired at G.M.'s expense. The cars in question include all the front-wheel-drive vehicles with manual transmissions manufactured by General Motors for the 1980 model year and the 120,000 1980 X-cars with automatic transmissions manufactured before May 1979. The cars are sold as the Chevrolet Citation, Pontiac Phoenix, Oldsmobile Omega and Buick Skylark.

Production of the nation's factories fell only one-tenth of 1 percent in December, the Federal Reserve reported today, giving a promising signal that the economy's longest decline since World War II may finally be touching bottom. Other positive news came on the inflation front, with a meager rise in December of one-tenth of 1 percent in the Producer Price Index for finished goods, the Labor Department reported. For the year, the producer index, a precursor of changes in consumer prices, rose only 3 1/2 percent, the smallest annual increase in 11 years and half the 7 percent rate in 1981. (Page 31.)

A State Supreme Court justice ordered the Rockland County sheriff today not to comply with a Federal Court order to give Federal authorities custody of a defendant in the Brink's robbery and murder case. The justice, Robert J. Stolarik, who is presiding in the case, said a Federal writ of habeas corpus ordering New York State to give up custody of the defendant, Samuel Brown, had frustrated the constitutional responsibilities of the Rockland County District Attorney, Kenneth Gribetz, and the sheriff, Thomas Goldrick. ''The Court does note,'' Justice Stolarik said in a six-page decision, ''that no authority whatsoever is cited by the Federal Government for what appears to be an unwarranted interference with an ongoing trial.''

A Soviet journal said today that Peking had undermined the fragile movement toward detente with Moscow by keeping longtime territorial claims and disputes alive and infusing its people with anti-Soviet sentiments. The commentary in the weekly political journal Novoye Vremya listed in detail the Chinese encyclopedias, textbooks and journals that continue to claim that the Soviet-Chinese border is the product of unequal czarist treaties and that great stretches of Soviet territory in Siberia and the Far East historically belong to China. It further accused the Chinese of failing to drop their customary accusations of ''hegemonism and expansionism'' against the Russians even while tenuous steps are taken toward normalizing relations. Western diplomats studying the article said they thought it might be a form of preliminary maneuvering for the consultations between the Chinese and Russians that are to start in Moscow in March.

With less than 12 months left before American medium-range missiles are due to be deployed in Western Europe, the Soviet Union has begun to fine-tune a campaign designed to block their emplacement and leave at least some of its 340 SS-20 missiles in place. Since Dec. 21, when Yuri V. Andropov, the Soviet leader, disclosed a major new proposal to keep the American weapons out of Europe, the Kremlin has been engaged in what amounts to a sophisticated public relations campaign. One pronouncement has followed another, each designed to persuade Western electorates that the Soviet Union has a plan to insure mutual security while the United States, as a Pravda editorial this week put it, seeks only to ''hoodwink'' Moscow. Subtlety of Soviet Approach Much of this is familiar to those who have followed the nuclear confrontation over the last three decades. But Western diplomats acknowledge that they are impressed by the increased subtlety of the Soviet approach.

President Reagan said today that he was determined to make progress in arms control and that the United States was now ''in a position to get somewhere'' in negotiating agreements with the Soviet Union. Mr. Reagan made his remarks in his first meeting with the press since he ordered the dismissal of Eugene V. Rostow as director of the Arms Control and Disarmament Agency on Wednesday. The President said he had made ''management changes so that we'll have a streamlined team'' that would help ''get results in the Geneva talks.'' The President said he wanted to ''straighten out the entire subject'' of arms control because there had been ''such disarray approaching chaos in the press corps'' on the subject.