What was going on when I was born?

New York City's Off-Track-Betting Corporation recently tried out a new high-payout wager: The Big Apple Double Exacta, in which a bettor had to pick finishers at both Aqueduct and Roosevelt Raceway. Harry McCabe, president of O.T.B., noted that ''for the first time in the history of racing, so far as I know,'' the trotting (Roosevelt) and thoroughbred (Aqueduct) establishments cooperated.

The threat from toxic waste that faces the nation is much more serious and will be much more costly to resolve than the Government has estimated, two Congressional research agencies have concluded. One report, released today by the Office of Technology Assessment, found that there were more than 10,000 disposal sites for hazardous waste around the country that would require cleanup on a priority basis to protect public health. This is substantially more such sites than the maximum of 2,500 the Environmental Protection Agency has estimated will have to be placed on its ''national priority list.'' Such sites contain toxic chemicals, metals or other hazardous substances such as radioactive materials.

CONFUSION about physicians' legal responsibility - and liability - when patients request not to be resuscitated appears to be the central concern prompting area hospitals to form committees on ''bioethics.'' The absence of Federal or state legislation that clearly defines terms and sufficiently protects physicians from latter civil or criminal suits in ''do-not- resuscitate'' cases has led in the past to what one physician describes as ''surreptitious'' ways of communicating and documenting such orders - an issue the new committees want to address. ''This is, of course, not a new problem,'' said Dr. Jerry Edelman, chief of medicine at United Hospital in Port Chester, where an ad hoc ''do not resuscitate committee'' was recently formed. ''The problem has been with us God knows how long - I guess since the first person had to make a decision about what to do.'' The reason it is now of growing concern, Dr. Edelman said, is that while the public has come to accept ''do not resuscitate'' as a legitimate choice for terminally ill patients, physicians often hesitate to comply. There are two reasons for this reluctance, he said.

TWO explosions killed at least 85 people in Shiite Moslem areas of Lebanon last week, igniting an angry reaction that included threats against Americans. Washington took the situation seriously.

IT was early January, and the County Board of Legislators was holding the first meeting of its 1985 session. ''Mr. Chairman?'' Anthony J. Giambruno, the Board's clerk, asked aloud, requesting the last of 17 roll-call votes on a procedural matter. But there was no reply. After waiting an appropriate length of time, Mr. Giambruno turned in his seat and looked up at the man newly installed at the large desk at the raised platform at the front of the legislative chambers. ''Ed,'' he whispered. ''That's you!''

Not many triangular buildings have been erected in New York, and few match the distinction of the Flatiron Building at Madison Square. But one, the old Cocoa Exchange building at the intersection of Beaver, Pearl and Wall Streets, erected in the 1920's, is an ornament of the Financial District, and now it has an assured future.

The Yankees, failing to appease Don Mattingly with a two- year, $1 million deal, renewed the contract of the American League batting champion tonight, prompting immediate bitter reaction from him. ''I'm disappointed that it had to come down to this,'' Mattingly, who will play for a $325,000 salary, said, aiming his words squarely at George Steinbrenner. ''The biggest disappointment was the way Jim Krivacs and I were treated the last three weeks. George didn't want to return calls or be talked to, then turned it over to Woody Woodward with two or three days left. It's something that I'll remember, the way we were treated. He showed me no respect the last three weeks.

The Milwaukee Brewers in 1972 had a coach named Jackie Moore and a struggling catcher named John Felske. Moore remembers Felske well. ''I remember that he reminded me of myself quite a bit,'' said Moore, whose major league catching career quietly expired after 21 games. ''He was trying to make the ball club and he was a very dedicated person, but he wasn't sure of his chances. I was the catching coach, and we spent a lot of time together. He went through this period where he wasn't sure he was going to quit baseball or what. The same thing happened to me. I went through the same kind of period. I don't want to take credit myself, but I might have had something to do with his staying in the game.''

THERE are many in Yaphank who recall the stir three years ago when The New Yorker published a cartoon depicting a Long Island Expressway exit sign for their hamlet. The sign read: ''Exit 66. Yaphank. If you have already been to Yaphank, please disregard this exit.'' One resident responded by placing a real sign near the expressway's Ya phank exit that read: ''Once you've seen Yaphank, you don't need The New Yorker.'' The implication of the cartoon was that Yaphank is a place ''time has passed by,'' said Linda Petersen, president of the Yaphank Taxpayers and Civic Association. Such an implication may not have been appreciated by many people, but to her it ''rang true, but rang true in a positive way,'' she said.

Eddie Murphy is coming back to his home town a superstar. With his ''Beverly Hills Cop'' breaking box- office records, Mr. Murphy is now the hottest actor in Hollywood, but finds appearing live in concert ''relaxing.'' Radio City Music Hall has scheduled him for five performances over the weekend of March 22. When ticket windows for the event were opened a month ago at 8 o'clock in the morning, all 36,000 tickets were sold within hours. Those who don't remember Mr. Murphy from his four seasons on NBC's ''Saturday Night Live'' had a chance to remind themselves of the Murphy style most recently when he returned to the show as a guest-host two months ago, smiling, cheerful but sassy, offering the audience advice as to which dolls to give children as Christmas presents. He displayed each doll in turn, noting regretfully that the G.I. Joe doll had shrunk from eleven inches to four inches. ''But as small as Joe is, he's still a macho guy,'' Mr. Murphy observed. ''Not like Ken here.'' Mr. Murphy lifted a Ken doll of the famous Ken-and- Barbie couple. ''Remember Ken?'' asked Mr. Murphy. ''Check out Ken's pink shirt, all right? Check out the way he combs his hair. And look at his posture.'' Mr. Murphy adopted an admonitory tone. ''Moms and Dads, unless you want your sons to live in the 'Village' and skip to work, keep them as far away from Ken as possible, all right?'' Wild hilarity and applause. Mr. Murphy then paired off a Barbie doll with macho G.I. Joe.

On Friday, the Government will report the retail sales figures for February. At least one forecaster, Money Market Services Inc., of Belmont, Calif., expects only a one-tenth of 1 percent improvement from January.

INSIDE, OUTSIDE By Herman Wouk 644 pp. Boston; Little, Brown & Company. $19.95 Herman Wouk has frequently proved his standing as one of America's premier storytellers. In novels, plays, motion pictures, and most recently a television series, he has captivated audiences, drawing on two main wellsprings -- a rich Jewish heritage and an interest in history. In this ambitious novel, his ninth, he charts the spiritual and social adventures of Israel David Goodkind, Yisroelke to his intimates. I. David to President Nixon, who in the fading days of his doomed second Administration brings him into the White House to provide imput on the Jewish and moral angles. Before reaching this exhalted position, Goodkind has been a student at Columbia University, the author of a varsity musical, a dramatics director at a summer camp, a highly paid gag writer for radio, a law student and a successful New York lawyer specializing in corporte taxes.