What was going on when I was born?

The woman sharing the compartment on the jolting train to Dresden said she would vacation in Hungary this summer. An East German, she planned to pay her way on holiday by selling in Hungary a pair of salamander shoes and a Carl Zeiss camera lens, both made in West Germany ''The barter is admittedly bothersome,'' she acknowledged, ''but I'm lucky to be going at all.'' Poland is off limits this year, she explained, and in Hungary and Czechoslovakia prices for things such as hotels, meals and gasoline have skyrocketed. Friends are staying instead on East Germany's windy Baltic shore, or in the nearby mountains.

A number of isolated incidents over the last few weeks have shaken faith in the world banking system, and many bankers fear that this erosion of confidence could be far more serious than the incidents themselves. Confidence is the core of banking. Without it even the strongest bank could not survive. And, the bankers say, that is true as well for the entire banking system.

Unemployment compensation funds in 16 states are experiencing painful cash squeezes and have to borrow regularly from the Federal Government to pay benefits to jobless workers. With the national unemployment rate at 9.5 percent, the highest in four decades, more than 4.2 million people are drawing benefits, an increase of a million and half in the last year. In addition to the 16 states, the District of Columbia, Puerto Rico and the Virgin Islands have had to borrow from the Federal Government, and before the economy recovers, about half the state funds are expected to have to turn to Washington for help. While Washington is obligated to aid states with short-term difficulties, new Federal rules severely penalize states that habitually pay out more in jobless benefits than they take in from employers. Many of these states, largely in the industrial North, are working urgently to revise their programs to lower the deficits and escape the penalties. Both New Jersey and Connecticut have substantial deficits, but New York, where benefits are significantly lower, has not run into trouble.

Tom Watson won his fourth British Open championship today and became the fifth golfer to win the British Open and United States Open in the same season. Won is the word that goes into the record books, but the fact is that the tournament was given to him by Nick Price. The 26-year-old South African collapsed on the final four holes with a double bogey and a bogey. As late as the 14th hole, Price was leading Watson by two strokes, and all he needed to do to win was to coast in with pars. Instead, he lost by one and finished in a tie with Peter Oosterhuis for second. ''I feel great empathy for Nick Price,'' Watson said. ''He gave me the tournament. This was not winning the way I did with the birdie on 17 in the U.S. Open. I've never been in a position where a man has given me a tournament from so far ahead.

Poland's military has been unable to turn the economy around after six months of martial law. Although returning visitors say food lines appear shorter, some Poles note that is because food prices have risen, while wages have been frozen. (Page A1.) In neighboring East Germany, curtailed deliveries of Polish coal to the chemical industry have pinched that nation's economy, while Soviet oil has been diverted to Poland, further aggravating the decline. Prices of imported raw materials have soared. (D1.)

Waiting for the recovery may take longer than some economists hadpreviously thought. That is the lesson emerging from recent economic reports, which add up to an economy that is still shrinking. Indeed, the recent barrage of unfavorable economic news, including declines in both retail sales and industrial production in June, is sending some economists back to their computers to reassess their estimates for the second quarter, which ended June 30. As a result, many of these economists now expect little or no growth for the rest of the year, an assessment that may become increasingly important as the politically sensitive election period approaches.

The Penn Square Bank, closed by Federal regulators two weeks ago, was known for a certain flamboyance. To woo officers of the big Northern banks to whom it ultimately sold more than $2 billion in energy loans, executives were in the habit of taking them to local Western bars, where, on at least one occasion, a top official entertained his delighted visitors by drinking beer out of a cowboy boot. In the heady atmosphere of good luck and fast bucks that has infected this petroleum stronghold since energy prices shot up nine years ago, the bankers' behavior hardly seemed aberrant. Diamond rings shaped like oil derricks became a common sight, a Rolls-Royce dealership opened and thrived and the price of deep natural gas reached more than 50 times what it would have fetched in the 1960's. ''It just got beyond any sensibleness,'' said Robert A. Hefner 3d, a leading wildcatter who has discovered hundreds of millions of dollars' worth of natural gas in recent years.

Joseph McCallion paced the corner of Second Avenue and 86th Street the other day, searching frantically for a police car. A worried look on his boyish face, a sheaf of papers in his hand, he was soon grumbling like any other New Yorker who needs a police officer and can't find one. But Mr. McCallion was himself an officer: a 21-year-old rookie who had just observed and written up his first traffic accident. All he wanted at this moment - and he wanted it very badly - was reassurance by some experienced officer of the 23d Precinct that he had done the right thing. ''I think I did all right,'' he said. ''It was street corner justice, but I think I did all right.'' Hundreds of rookies like Officer McCallion, who graduated from the Police Academy on June 25 in a class more than twice the size of any other in recent years, have taken to the streets of the 23d and other precincts to learn their job. By the fall, most will be absorbed into precinct commands throughout the city and will generally be riding in patrol cars. Many will take the place of retired officers or others who have moved into specialized units ranging from narcotics to harbor patrol.

President Reagan's appointment of four new judges for the Federal appeals court in Manhattan constitutes the most sweeping change of the court's membership in more than a decade. By filling four vacancies, the President has selected a substantial part of the 11-member appeals court in an unusually short time. But the new appointments do not appear to foreshadow a sharp shift in the court's judicial philosophy. The court, the United States Court of Appeals for the Second Circuit, handles Federal cases in New York, Connecticut and Vermont. It has shaped much of the nation's commercial law from its Manhattan base in the center of business and commerce.

Three players making comebacks of different sorts exceled yesterday in the Yankees' 7-3 victory that completed a four-game sweep of Billy Martin's sagging A's. Rick Cerone, playing his second game since coming off the disabled list, got two hits, including a homer; scored three runs and batted in two. Ron Guidry, who came into the game with a 1-3 record and a 5.47 earned run average in his last nine starts, pitched six and one-third strong innings in the blazing heat and picked up his first victory since June 14 for a 9-4 overall record. Rudy May, on the verge of being dropped in recent days to clear a roster spot, retired the final eight batters, three on strikeouts. Manager Gene Michael characterized the Yankees' play since the All-Star Game break as their best of the season, even better than a stretch in late May, when they won nine of 10 games. In the series with the A's, all four starters - Guidry, Shane Rawley, Roger Erickson and Mike Morgan - pitched sharply, and the hitters, quiet through most of the first half of the season, produced six homers.

The hottest day of the year baked the pavements and parks of metropolitan New York yesterday, sending residents fleeing to anything wet, cold or air-conditioned. The National Weather Service could only guess at the Manhattan temperature; its recorder in Central Park had stopped working Saturday night. However, Tom Grant, a meteorologist with the service, said that the 98 degrees recorded at La Guardia Airport at 3:50 P.M. was pretty much the temperature everywhere. More than three million people jammed the beaches: Coney Island, Riis Park, Jones Beach, Orchard Beach and the Rockaways all reported capacity crowds, and some had to close by midday for lack of room.

Israel has officially acknowledged to the United States that it used cluster bomb weapons in its invasion of Lebanon, but has asserted that its actions were consistent with Israeli-American agreements on the use of those weapons, according to Israeli sources here familiar with the message. The Israeli note was delivered Friday night, and White House and State Department officials said this afternoon that it was still being reviewed. They said ''no final decision'' had been made on whether to go ahead with a planned delivery to Israel on Monday of 4,000 rounds of cluster munitions designed for use in 155-millimeter howitzers. Some Administration officials said, however, that they anticipated at least a delay since they doubted that the review would be concluded by Monday.