The Securities and Exchange Commission, which demands good accounting in the corporate world, has considerable trouble keeping its own books, according to a report this week by federal auditors.

A $58 million accounting problem here. A $102 million mistake there. A $452 million item somewhere else that was not properly disclosed until the auditors caught it.

A review by the Government Accountability Office found “a litany of issues . . . which frankly the SEC should have prevented or detected on its own,” said Jeannette Franzel, a managing director at the GAO.

The problems are not new: Auditors have been issuing warnings about the SEC’s internal accounting for years, and the SEC has acknowledged weaknesses. But the situation worsened in 2010 as temporary patches failed, according to GAO officials.

Instead of trying to rebuild its troubled systems, the SEC has decided to outsource its financial reporting to another part of the government, the Department of Transportation.

That will not solve the problem completely, because some of the work must still be done at the SEC, auditors said.

The GAO report pertained to the SEC’s financial reporting, not its performance regulating companies and markets, SEC spokesman John Nester said.

The commission’s chairman, Mary L. Schapiro, recently told a Senate Committee that the weaknesses at her agency were “unacceptable.” She said they were caused by “years of underinvestment in financial systems technology.”

Experts say there are many reasons for concern when an agency’s accounting is in disarray. The agency could wind up spending money that it doesn’t have, for instance. Congress could be handicapped as it tries to oversee the agency’s performance or make decisions about its budget. What’s more, someone trying to disrupt the agency could tamper with numbers.

The GAO concluded that, after various errors were caught, the financial statements the SEC issued for 2010 were accurate. That was not a vote of confidence.

“We found that they are at risk that they could get it wrong in the future and not know it,” Franzel said.

Some parts of the federal government are in worse shape than the SEC. For the 2010 fiscal year, the financial records of the departments of Defense, Labor and Homeland Security were in such disarray that they could not even be audited, according to the GAO.

Unlike those departments, the SEC is in the business of regulating accounting and auditing, making its shortcomings particularly problematic.

In a March 29 letter to the SEC chairman, the GAO detailed an array of glitches.

The agency collects fines in enforcement cases, and it distributes that money to the U.S. Treasury or to investors who were victims of the fraud. But it essentially lost track of $102 million, failing to record that it had been transferred to the Treasury, according to the GAO.

The SEC was supposed to provide details about the finances of an investor protection fund, but as it drafted its financial disclosures it neglected to break out a $452 million item until the GAO noted the omission.

In many cases, SEC personnel paid contractors’ bills without proper approval. More than half of the 67 “non-payroll disbursements” that auditors examined had been handled improperly.

The agency is supposed to collect interest on delinquent fines assessed in enforcement cases. But when it came to fines ordered by federal courts, the SEC did not record the amount of interest it was owed until the fines were paid.

As of the middle of last year, $464 million of interest on court judgements was delinquent.

The GAO letter also highlighted the fact that many of the penalties the SEC trumpets are never collected. Some alleged wrongdoers may lack the funds.

As of Sept. 30, the SEC was owed $657 million in fines and “disgorgement” — the surrender of ill-gotten gains — but the agency expected that $575 million of that would go uncollected.

The GAO also warned that the SEC is exceptionally vulnerable to a calamity. A key administrative center in Alexandria and another facility for backup data are located so near each other that both could be taken out by the same disaster.

In a written response to the GAO, Schapiro said the SEC “is committed to investing the time and resources to put its internal controls over financial reporting on a strong, sustainable path.”