In the wake of the run on savings and loan institutions in Ohio, some observers have gone to great pains to argue that, overall, the American financial system remains basically sound and stable. Thus, we are told, there were only 79 failures last year among 14,700 commercial banks. And only nine of 3,146 federally insured thrift institutions went broke.

These numbers are accurate, but do not tell the whole story. The 79 bank failures last year represent the biggest number since the Great Depression. Moreover, some 900 of the 14,700 are listed as "problem" banks by the Federal Deposit Insurance Corp. This "sick bank" list is 2 1/2 times as big as it was at the end of 1982. And 335 of the 900 are agricultural banks -- many of which got their bad ratings in the last year.

On a scale of 1 to 5, in which "1" is healthy and "5" a high probability of failure, these 900 are rated either "4" or "5." According to officials, most of the 900 are in category "4," which means that the risk of failure is significant, "but is not yet imminent or pronounced."

As for the savings institutions, even though only nine thrifts covered by the Federal Savings and Loan Insurance Corp. failed last year, 64 others were merged out of existence either voluntarily or involuntarily last year. Even more thrift institutions -- 672 -- disappeared in 1982 and 1983.

Earlier this month, Financial Corp. of America, the giant thrift holding company based in Los Angeles, had to boost the interest rates it pays on deposits in an effort to regenerate confidence after announcing that its losses last year would run between $550 million and $700 million.

At almost the same moment, one of the most respected banks in the nation, Texas Commerce Bancshares Inc., was embarrassed by a large bad loan to a partnership that included one of its own directors. BankAmerica had to write off a huge loss for bad mortgages. The Bank of Boston and two other prestige- drenched banks in that city had to admit to irregularities in reporting cash transactions, and the Bank of Boston admitted handling cash for reputed organized-crime figures.

Last week, First City Bancorp. of Texas disclosed that federal regulators had declared "inadequate" the internal controls on problem loans at three of the company's largest banks, including First City National of Houston, its flagship bank.

On Tuesday, Chemical Bank of New York disclosed that it voluntarily had told the Treasury it had violated government cash-reporting rules designed to prevent money "laundering" to the tune of $26 million. Chemical Bank voluntarily disclosed this information to the Treasury, presumably to avoid the bad publicity suffered when the Bank of Boston news broke.

So a lot is going on in the banking/thrift system, not all of it good, and it's natural that the government wishes to assure citizens of the overall soundness of most financial institutions. No one, and that includes this reporter, wishes to paint an overly grim picture that would cause panic, or a run. Officals at the Federal Reserve Board are known to have been upset by comments made 10 days ago on the Phil Donahue television show, raising questions about the soundness of the banking system. Their beef was that the Donahue program merely "stirred things up."

But the average citizen has a right to be aroused by the discovery that deposits thought to be "insured" or "guaranteed" are not always safe, and it is high time that this concern evidenced itself.

For example, as New York economist Henry Kaufman points out, the quality of federal regulation and regulators has deteriorated. This has happened because financial regulatory agencies "have been relegated to a secondary status in the past decade or so," the result being that the most competent government workers either go to more visible policy-making agencies, or get better-paying private-sector jobs.

It would be a bad mistake for officials to suggest that the Ohio closings and the failure of E.S.M., a small securities dealer in Florida now accused of fraud, are aberrations in an otherwise strong system. The public was quick to grasp the significant point: This was but one piece of a continuous cycle of events.

Under deregulation, managers of banks and thrift institutions have been encouraged to take greater risks -- they have to, in order to be able to pay the higher interest rates available in a competitive market. "We have to make sure that depositors are protected if management takes those risks, or else limit the risks banks can take," Felix Rohatyn, senior partner of Lazard Freres of New York, said in an interview.

In a dramatic way, when those 71 thrift institutions in Ohio were forced to close, it exposed the fragility in today's financial structure, and it's not limited to those institutions -- like those in Ohio -- which had private, rather than federal, insurance.

The more than 3,000 federally insured savings and loan associations are a better risk than private-insured institutions, because the good faith and credit of the United States government implicitly stands behind the FSLIC. But all S&Ls, including the federally insured institutions, have been weakened by the inflated- interest-rate structure that has sharply cut the value of the outstanding mortgages they had issued at lower rates in years gone by. The true net worth of many S&Ls is vastly less than stated on the books.

If S&Ls and other financial institutions had to value more of their assets at what they are really worth, it would induce more conservative lending practices. This applies, as well, to major American banks that have a huge and still risky exposure in their Third World loans, some of which never will be repaid.

What the S&L depositors in Ohio discovered was that a sign on the door saying "Fully Insured" is meaningless. Government, as Kaufman suggests, must develop a credit-rating system for all banks, S&Ls, credit unions and so on that it is willing to make public. We need full disclosure. Today, they tell us that these institutions aren't safe only after they close or merge them.