THE Salomon Brothers' misconduct in the Treasuries market -- coming after such scandals as the fall and bailout of hundreds of savings and loans, the drug and money-laundering and bribing activities of the Bank of Credit and Commerce International, the junk bond debacle of Drexel Burnham Lambert and the assorted frauds in the Japanese stock market -- has further stirred anxieties about the integrity of financial markets. Unless they are quelled, such anxieties could hurt saving and investment all around the world.

In cracking down hard on Salomon Brothers for exceeding the 35 percent quota for primary dealers in the auction markets for Government securities, the Treasury was sending a message to the other 39 primary dealers in that market that conduct like Salomon's would be dealt with harshly. With $2.3 trillion in Federal debt to be marketed and rolled over ad infinitum -- a debt total that is expected to increase by $279 billion in the fiscal year 1991 and by $362 billion in 1992 -- any loss of faith in the integrity of the Government securities market might be extremely costly.

Treasury Secretary Nicholas F. Brady, in an interview on Tuesday, said he did not know how "deep" the problems in the Government securities market went. The Treasury, he said, was not an investigative agency; the S.E.C. and the Federal Reserve, on which the Treasury depends, are now "collecting information." But Mr. Brady is clearly warning every house that might be acting as Salomon was to clean up its act fast.

He was asked why the Treasury, having first announced, at 10:30 Sunday morning, that Salomon had been barred from bidding in the primary Treasury auction market, said five hours later, following a telephone conversation between Mr. Brady and Warren E. Buffett, the firm's new chairman, that Salomon could bid for its own account but not for its customers. Mr. Brady replied, "In substance, that changed the situation only marginally."

At the time of the first announcement Sunday morning, he said, there had been only "a lot of talk about what might happen," but no concrete action. By the time of the second announcement, said a Treasury official, who requested anonymity, the Salomon board had taken four actions: (1) Dismissed the top three executives -- John H. Gutfreund, the chairman; Thomas W. Strauss, president, and John W. Meriwether, vice chairman; (2) discharged the head of the Government trading desk, Paul Mozer, and his No. 2, Thomas Murphy; (3) announced other administrative and management changes, and (4) pledged, through Mr. Buffett, to cooperate fully with the Treasury, S.E.C. and Fed, to "right the wrongs." Mr. Buffett gave Mr. Brady his personal assurance that the situation at Salomon would be cleared up.

Mr. Brady denies that confidence in United States securities has been shaken. He said that the Federal deficit was "too big" but that the United States was able to sell its obligations to the world. "The enormous amount of our bonds people buy," he said, "imply confidence not only in United States securities but in the method by which we distribute them, directly and with dispatch."

Instead of damage to the United States resulting from the Salomon scandal, he said, the way it was being handled would "enhance everybody's confidence." The United States financial market, he said, is "deep and liquid -- I'm not sure whose exceeds it."

But with financial markets having gone global on a 24-hour-a-day basis, don't investors need better international regulation? "Good question," Mr. Brady said. But he added, "We have to rely on the individual countries." Every country, he noted, has its own rules and codes. He conceded that it might be desirable to negotiate standard regulations at least for the principal financial markets.

He cautioned against overregulating financial markets, contending that "the cure can be worse than the disease being cured." The United States, he said, now has the opportunity to "do it right" and show that "our market is the safest in the world."

Did he have any new thoughts on how to bring the climbing budget deficit down? He said the worsening of the projected deficit for 1992 was the result of to the "vagaries of the S.& L. bailout and Desert Storm," but he had "confidence that in the long run -- that is, the next five years -- the outlook was for the deficit to slope downward."

Official projections support that view. The Congressional Budget Office projects the deficit will peak at $362 billion in the fiscal year 1992 and fall to $156 billion by 1996.

The Administration's Office of Management and Budget sees a peak deficit of $348 billion in 1992 and expects a surplus of $20 billion in 1996.

Herbert Simon, Carnegie-Mellon's Nobel laureate in economics, says, "If you can't forecast, stay flexible." And Treasury Secretary Brady, the nation's premier bond salesman, seems to be saying, in the wake of the Salomon scandal: If you can't forecast the public debt, just be sure you can sell it to the world.