June 6, 1982

LESS than 10 years ago, assistants in the Suffolk County Attorney's office, many of them political appointees, worked out of their private law offices, with the county paying half their rent and half the salary of a secretary. Now, confronted with a growing caseload, the County Attorney's office has taken on the trappings of professionalism, with all the assistants in county buildings, although most of the 43 attorneys are still political appointees. William Kent, the chief deputy county attorney, said that major factors behind the growing caseload were the county's changeover to self-insurance in most cases and the tangle of Federal regulations, particularly in social services. The office, he said, was handling cases from the prosecution of juvenile delinquents to the defense of major negligence suits.

Until yesterday, only three horses in this century had won the Belmont Stakes by more than 10 lengths: Secretariat, Count Fleet and Man o' War. Now there is a fourth, and if he keeps running the way he did yesterday, he may someday be mentioned in the same breath as those three thoroughbred idols. Conquistador Cielo, who ran the fastest mile in the history of Belmont Park only six days ago, was leading a top field of 3-yearolds by only a head after the first mile of the 114th Belmont Stakes yesterday at Belmont Park. Half a mile and 50 4/5 seconds later, he crossed the finish line under Laffit Pincay Jr., 14 1/2 lengths ahead of Gato del Sol, the Kentucky Derby winner. The track was reduced to a sea of mud by downpours Friday night and yesterday afternoon, but nobody was making excuses. ''Nothing would have made a difference today,'' said Eddie Delahoussaye, who rode the runner-up. ''The winner was just too much.''

WHILE Connecticut's six United States Representatives are busy shuttling between Washington and their districts, watching the political developments at home and preparing a record in office on which they can seek re-election, they are facing a difficult, confusing and overdue piece of business that will probably reach the top of the agenda later this week: the 1983 budget. The House of Representatives was supposed to make the basic decisions about the budget last month, before the Memorial Day recess, voting on a ''budget resolution'' that would lay out the broad outlines of tax and spending changes. But with three proposed resolutions before them - one from each of the parties and one bipartisan effort - the Representatives failed to reach agreement before they left the Capitol. However, in a series of interviews with The New York Times just before the recess began, the state's six Representatives and two Senators showed a surprising degree of agreement on several outstanding issues.

For several months it has been taking shape behind whitewashed windows at 1191 Third Avenue, looking to passersby like yet another boutique aborning in a neighborhood of boutiques. But now the windows have been washed clean, a uniformed guard is at the door and everyone can see what the first new private safe-deposit vault in New York City in 20 years looks like.

The ink stain on the front of George Bamberger's shirt, right under where it says Mets, was a sign that he had been doodling during the game tonight. The 6-2 loss to the Reds was the fourth straight defeat for the Mets, tied their longest losing streak of the year, and was evidence that some changes were in order. The names Bamberger scribbled on the back of tonight's lineup card formed tomorrow's lineup. The Mets manager would not say whose names would be on the dugout wall Sunday, but he did say there would be changes.