April 10, 1983

FOR centuries, commercial fishermen along the shores of Long Island and Connecticut have shared the productive fishing grounds of Long Island Sound. But when Connecticut's State Department of Environmental Protection introduced a proposal last month aimed at resolving a highly controversial dispute among fishermen, the proposal and the dispute erupted into Long Island waters and onto the Island's multimillion-dollar commercial fishing industry. The dispute began two years ago in the fertile lobster nursery grounds west of Stratford, when two Connecticut fishing vessels initiated a new fishery in Long Island Sound - trawling for lobsters. The trawl fishermen, who tow a cone-shaped net over the bottom in search of fish, have always brought up lobsters as a bycatch from time to time. But the trawlers' pursuit in the Sound has been fish, not lobsters, which have traditionally been harvested from the pots of the lobstermen. The venture proved to be a success for the two lobster trawlers, which reportedly boasted a catch for a day's trawling of more than 1,000 pounds of lobsters. However, last fall the issue intensified as their efforts and their numbers increased.

The New York City Board of Education yesterday selected Deputy Mayor Robert F. Wagner Jr. to serve as the 14th chief administrator of the country's largest public school system. The vote, which followed a bitter two-month campaign that took on racial overtones, was 6 to 1 for Mr. Wagner, who was Mayor Koch's candidate to succeed Frank J. Macchiarola as Schools Chancellor. The seven-member board will meet Wednesday to adopt a resolution formally naming Mr. Wagner as Chancellor. It will also ask the State Education Commissioner to grant Mr. Wagner a waiver because the 39-year-old Deputy Mayor does not meet all the formal qualifications for chancellor as set down in state education law. Joseph G. Barkan, president of the board, announced Mr. Wagner's selection at a news conference after a morning of deliberations in private at board headquarters at 110 Livingston Street in Brooklyn.

GOVERNOR KEAN'S first term is far from its halfway mark, but ''testing the waters'' already has become the newest political ''in'' phrase. In fact, the New Jersey Election Law Enforcement Commission has scheduled a public hearing for May 11 to examine its proposed changes in the state's campaign contribution and expenditure regulations. The changes would allow ''testing the water'' bank accounts by potential opponents of Mr. Kean, should he decide to run for a second term in 1985. The term refers to the activities a potential candidate goes through before deciding whether to formally announce his or her candidacy. Among these are polling, traveling, attending conferences and distributing newsletters.

The space shuttle Challenger, bucking 18-knot headwinds, glided to a smooth landing here today for the successful conclusion of its first flight. Officials of the National Aeronautics and Space Administration hailed the virtually trouble-free performance of the nation's newest space shuttle on its five-day flight and moved to hasten its ground servicing for another flight in two months. Only such a rapid turnaround will make it possible for the agency to meet its commitments to fly four more shuttle missions this year. Previously, the shuttles have required four or more months between flights. 'A Superb Spacecraft' At a post-landing news conference, Lieut. Gen. James A. Abrahamson of the Air Force, an associate administrator of the space agency, called the Challenger ''a superb spacecraft.'' Only 22 anomalies were reported in the flight, as against 82 on the first flight of Challenger's sister ship, the Columbia.

Scholars have categorized ''All's Well That Ends Well'' as one of the Bard's ''problem plays,'' as puzzling as ''Measure for Measure'' and ''Troilus and Cressida'' yet less stimulating than either, and over the centuries actors and directors have remained faithfully aloof. ''A nasty play,'' wrote the eminent critic Sir Arthur Quiller-Couch, who edited ''All's Well'' in the definitive New Cambridge edition. Indeed, the first recorded performance of ''All's Well'' took place 125 years after its author's death, and major revivals since then can be counted on, well, a hand and a half. Enter the Royal Shakespeare company, which presented ''All's Well'' here in 1981 in a late-Edwardian setting that came complete with steam locomotives, goggled aviators, nightclub chanteuses, waltzing courtiers, bursting shells, Red Cross nurses, and much else that its author omitted to specify in his stage directions. And the result? The critics were mostly ecstatic and the houses were packed, first in Stratford, then in London. Now Broadway will have its chance to assess a production which, as it happens, comes from the same sharp and abundant imagination as the one principally responsible for ''Nicholas Nickleby'' and ''Cats.'' ''All's Well That Ends Well,'' staged by the RSC's Trevor Nunn, opens a 16-week engagement at the Martin Beck on Wednesday.