While George W. Bush was president, the U.S. Coast Guard signed a contract to get administrative help from a company in Northern Virginia. It paid $144,000, and the contract was completed by June 30, 2005.

Twenty years passed. Presidents came and went.

Last week, Elon Musk’s restructuring team, called the Department of Government Efficiency or DOGE, said it had just canceled the long-dead Coast Guard contract — and in doing so, saved U.S. taxpayers $53.7 million.

That claim, posted on the group’s “wall of receipts,” bewildered experts on federal contracting. And there were others like it. Even after Mr. Musk’s group deleted several large erroneous claims from its website last week, The New York Times found that it had added new mistakes — claiming credit for “canceling” contracts that had actually ended under previous presidents.

“These are not savings,” said Lisa Shea Mundt, whose firm, The Pulse of GovCon, tracks federal spending. “The money’s been spent. Period. Point blank.”

These mistakes do not mean DOGE has not made cuts to the federal government. It has, deeply, by pushing widespread layoffs of employees and cancellations of active contracts, and by helping instigate the demise of the U.S. Agency for International Development.

But the repeated errors have raised questions about the quality and veracity of the information that the Musk team is putting out, including whether it is being misled by other departments. The mistakes also seem to call into question the team members’ competence — whether they understand the government well enough to cut it while avoiding catastrophe.

“It’s obvious that they don’t understand,” said Eric Franklin, the chief executive of the firm Erimax, who advises the government on contracting procedures. His own firm was the subject of one of the errors on DOGE’s “wall of receipts.” Mr. Musk’s group claimed it had saved $14 million by canceling one of its contracts — which had ended in 2021.

“It’s really akin to a bull in a china shop,” Mr. Franklin said. “And what do you end up with? It’s just a big mess.”

At the White House, a senior administration official offered a partial explanation, saying the information on the wall of receipts had been provided by individual federal agencies — many of which have embedded staff members from Mr. Musk’s group. The official, who spoke on condition of anonymity because he was not authorized to describe DOGE’s methods, said Mr. Musk’s group then checked the accuracy of the agency’s claims.

Why were there still so many errors? The official said individual agencies should answer that question. On its website, DOGE says it is trying to improve its data, and asks readers to notify it of potential errors.

Agencies are under tremendous pressure to find budget cuts for Mr. Musk’s group to promote. The group has even created a “leaderboard” to measure which ones have eliminated the most.

But in databases of federal contracts, there are clues that this rush is not being well managed or adequately tracked.

In the past, the government has designated specific codes to track large batches of contracts across different agencies that relate to a common initiative, like the federal response to the Covid-19 pandemic. That makes it easier to find all the contracts involved.

But the contracts in the “wall of receipts” have no such signature. That omission may mean there are errors in both directions — not only with expired contracts that don’t actually save money, but also potentially with contracts that were canceled by the group’s effort but are not being counted.

Mr. Musk’s group has said that it has saved taxpayers $65 billion, by cutting contracts, leases, federal employees and other items in the federal budget. But it has itemized only two of those categories: cancellations of contracts and leases. When adding up DOGE’s claimed savings for each item, those categories collectively account for about $10 billion, less than one-sixth of the total.

When DOGE first published its list of canceled contracts, there were about 1,100 examples.

The five largest were wrong.

In one case, DOGE listed a contract worth $8 million as actually being worth $8 billion. In another, it mistakenly counted the same $655 million contract three times. In yet another, it erroneously said that a huge contract at the Social Security Administration had been fully canceled, saving $232 million. In reality, only a small project within that contract had been canceled. Actual savings: $560,000.

By last week, all of those claims were gone. DOGE revised the total savings from these five cuts from $10 billion down to about $19 million.

At the same time, Mr. Musk’s group also added about 1,100 new canceled contracts to the list.

Among the new entries were several that had ended before President Trump took office.

Mr. Musk’s group took credit for the cancellation of a $1.9 billion Treasury Department contract, for work on information technology at the Internal Revenue Service. But it had actually been canceled in November, when President Biden was in office.

The Treasury Department suggested this cut to DOGE in a post on X on Feb. 19. Two days later, The Times reported that it had been canceled before Mr. Trump took office.

Three days after that, DOGE went ahead and posted the Biden-era cancellation on its wall. The Treasury Department did not respond to questions about the contract.

DOGE also claimed credit for canceling two different Coast Guard contracts that had ended during the George W. Bush administration. In addition to the $53 million contract that ended in 2005, Mr. Musk’s group said it had saved $53 million more by canceling another contract with the same vendor. Public contracting data shows that one ended in 2006.

Deniece Peterson, a senior director of federal market analysis at the firm Deltek, said that both contracts were part of a larger spending agreement with a $53 million spending limit. In all, she said, the Coast Guard paid the vendor about $35 million over several years. All of its work under that agreement was completed by 2011, and federal contracting data shows that no bills remain outstanding and no more money was expected to be spent.

Tricia McLaughlin, a spokeswoman for the Department of Homeland Security, did not offer an explanation for why the department had claimed $106 million in savings from ending these two long-dead contracts. Instead, she responded to questions from The Times with an email saying: “We’re certainly excited about $100 million + in taxpayer savings.”

And then there were the links on the DOGE website that led to different contracts than those touted.

DOGE claimed it had saved $149 million by canceling a contract for three administrative assistants at the National Institutes of Health worth about $1.4 million.

The link, however, led to the page of an unrelated contract with a different company that supplies refrigerated gases used in laboratories. That contract, which does not appear to be canceled, was worth only $118,000.

After being asked about the errors, an official with the Department of Health and Human Services said DOGE was working to correct the website.

Emily Badger contributing reporting.