June 14, 1981

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.