What was going on when I was born?

JERSEY CITY VOTERS here have been to the polls twice in the last month, but they still must go one more time - on Tuesday - to finally elect a Mayor. The month that began with the first mayoral election on May 12 has been one of the most dramatic in recent local political history, and has seen the political fortunes of Walter N. Sheil and Thomas F.X. Smith ebb steadily. When it began, Mr. Sheil was the Hudson County Democratic chairman and a State Senator who was running for Mayor here; Mr. Smith, the incumbent Mayor, was running for Governor. The two men held whatever broad political power there was in the county.

It was a bright October afternoon in 1979. On her way out of the house, Naomi Graffman stopped to look in on her husband, the pianist Gary Graffman, as he finished practicing the Brahms Piano Concerto No. 2. The strange mistakes that had crept into his playing over the past year made the music almost unbearable to hear. As the last notes sounded, she invited him to come out for a walk. He was reluctant. There was a Beethoven concerto still to work on. ''Oh, Gary, please come out,'' his wife coaxed. ''It's such a gorgeous day.'' ''Well, at least I can still play the Beethoven,'' Mr. Graffman remembers thinking as he got up from the piano. ''I guess I can go out for a walk.'' They strolled out of their midtown Manhattan apartment house into the sun, walking a few blocks in near silence. Then, suddenly, Mr. Graffman turned to his wife. ''Something's wrong,'' he blurted out. ''It's been wrong for a long time. And it's getting wronger and wronger.''

Inflation Forecasts Rosier Luck and the business cycle are working to push inflation projections down - 'way down. Inflation forecasts are falling like a stone.

''Twenty-five years ago this was a dusty twolane road and nobody seemed to want to build anything but houses here,'' said Jerry Spiegel one recent afternoon as he maneuvered his car through traffic on North Broadway, Hicksville's six-lane thoroughfare. ''Today this is one of the main commercial and industrial corridors in Nassau County and now anyone who wants to be here today has to come to me.'' Mr. Spiegel has the largest concentration of commercial and industrial space under individual ownership on Long Island. With the exception of the Mid-Island Shopping Center and the Sears store, Mr. Spiegel owns most of the property along Route 107-North Broadway between the Long Island Expressway and the Hicksville train station. In addition to that mile-long strip, which includes office buildings, banks, gas stations, shopping centers, fast-food establishments, showrooms and light industrial businesses, Mr. Spiegel has developed hundreds of other commercial and industrial sites in both Nassau and Suffolk Counties over the last two decades. Almost all of his buildings are small, one- to three-story projects.

THE BACKBENCH DIARIES OF RICHARD CROSSMAN Edited by Janet Morgan. Illustrated. 1,136 pp. New York: Holmes & Meier. $35. Diaries are a special kind of addiction. The real addict likes as much detail as possible so he can indulge in total immersion. It doesn't matter if there are hundreds of minor characters whose names no one can remember, provided the central character constantly develops with as many quirks, prejudices and oddities as possible.

LOS ANGELES When ''Superman II'' opens in 1,354 American and Canadian theaters next Friday, it will already have sold $100 million worth of tickets on the planet the comic-book character has saved more than 100 times during the last 43 years. Two years from now, unless production is delayed by Hollywood labor disputes or some unforeseen catastrophe, ''Superman III'' will be opening in an equal number of theaters. Christopher Reeve has already signed his contract as Superman. Richard Lester, the director of ''Superman II,'' is close to signing his. And Ilya Salkind, the producer who has renewable options to make movies about the invulnerable Man of Steel until the year 2000, envisions a saga of four, six or even eight Superman movies. ''Like 'Star Wars,' '' Mr. Salkind says. According to Mr. Salkind, the first two Superman movies have cost $109 million. He has, at various other times, estimated the cost as $120 million or $140 million. ''This is the catastrophe of the situation,'' said Mr. Salkind, ''that movies that made so much money are still in the red.''

LOWER ALLOWAYS CREEK AT 4:43 A.M. on June 5, before dawn warmed the bleak, marshy lowlands along the lower Delaware River and highlighted the hulking forms of the two reactors here, another nuclear station, Salem II, silently slid on line. Finally licensed on May 20 after a 25-month delay - and at a time when no new nuclear plants have been started and plans for more than half a dozen throughout the country have been canceled - approval of the Public Service Electric & Gas Company's Salem II unit may be something of an anomaly. Or, it may indicate that the logjam in nuclear-plant applications that developed after the accident at Three Mile Island in March 1979 has finally broken up. While Public Service officials are still grumbling that the delay cost them $200,000 a day, local opponents of nuclear power worry that the permit might have come too soon; that is, before full completion of the safety-related tasks that the Nuclear Regulatory Commission assigned to Public Service as a condition to granting it a license. Public Service's elation over getting the plant on line was dimmed somewhat when about 3,000 gallons of ''low-level radioactive'' water spewed from a leaking vent valve into a containment basin. The unit was on standby - not producing power - at the time.

The huge salary offers made to free agents under the new right of first refusal, coupled with a shocking report of increasing losses, has stirred fear among National Basketball Association owners. Reports say that several teams are for sale and that owners, for the first time, are openly worried that several franchises may fold unless buyers are found. Among the teams reportedly for sale are the Indiana Pacers, Denver Nuggets and Detroit Pistons. A report by Arthur Andersen, an accounting and consulting firm, said that the collective losses for the 23-team league for the 1979-80 season jumped in one year from $8 to $13 million. In the annual report, which is always a season behind, each team submits a financial statement. The report does not cite losses of individual teams, but rather the total losses in the league. Those problems were discussed at the recent annual meeting of owners at Cambridge, Mass., where, it was learned, the following occurred: - Larry O'Brien, the N.B.A. commissioner, formed a committee ''to consider what steps may be taken to insure the financial stability of the league.'' The committee was given 30 days to report its findings to O'Brien and his advisory committee, composed of Mike Burke of the Knicks, Arthur Wirtz of the Chicago Bulls, Dick Bloch of the Phoenix Suns, Abe Pollin of the Washington Bullets, Bill Davidson of the Detroit Pistons and Larry Weinberg of the Portland Trail Blazers.

New York City distinguished itself from the rest of the country in two important housing categories in the 1980 census - one of them indicating poverty and the other, wealth. Government and private analysts say that taken together, the findings show that the city has some serious housing problems, including a growing gap between housing for the poor and housing for the rich. ''There really are two cities in New York,'' said George Sternlieb, director of the Center for Urban Policy Research at Rutgers University. ''We've always had a city of contrasts, but never have they been so sharp as now, because now there is no middle.''

MINEOLA FOLLOWING the recent layoff of nearly 2,000 CETA public service employees in Nassau and Suffolk Counties because of budget cuts by the Reagan Administration, local government and business leaders are calling on Washington to create a ''new'' CETA with the emphasis on private industry. These leaders are seeking to transform the trouble-plagued program into a job-training effort that will aid the economic recovery not only of the Island but also of the whole United States, by taking the burden off the public payroll and putting people on the private payroll, thus generating new tax revenues. The Nassau County Executive, Francis T. Purcell, has been a staunch backer of President Reagan's cuts in the Comprehensive Employment and Training Act program, but he supports the CETA objective, which is to provide training and jobs for the disadvantaged and unemployed. Mr. Purcell's main objection to the program's old format was its dependence on public service employment. So, when the recent budget cuts forced Nassau to lay off 300 CETA workers, he was glad the county had not hired more.

Philip C. Habib, the special American envoy, traveled to Saudi Arabia today after five quiet days in Beirut, his Middle East peace efforts cast into doubt by the Israeli bombing of an Iraqi nuclear plant. Mr. Habib left here at 11 this morning, with American officials refusing to disclose his destination. The Saudi press agency reported his arrival in Jidda late this afternoon. The United States is pinning much of its hope for defusing the Middle East missile crisis between Israel and Syria on the possibility that the Saudis will be able to exert some form of moderating influence on the Syrians.

A house on a corner seems to invite the unusual. Baldur and Friederike Peter, who purchased their Smithtown, L.I., home eight years ago from a doctor, say that former patients frequently ring the bell because they remember the corner, but do not remember that the doctor has moved.moved. One morning, the Peters also discovered a car in the middle of their front lawn. The driver, a woman, had skidded while trying to negotiate the turn. She was unhurt, but their lawn and a tree needed repair. Corner lots are known not only for being rammed by cars, but also for being used as shortcuts. Lesley and Nicoletta Lorant, who live in a corner house near Poughkeepsie, N.Y., are resigned to watching dunebuggy drivers to teen-agers on dirt bikes use their front lawn to cross to another road. However, their wedge-shaped property has also served a better cause. Friends who own a hot-air balloon have found it a perfect site for takeoffs.