The Reagan administration's drive to sell off surplus federal housing, already the subject of a grand-jury probe in Camden, N.J., has been plagued by mismanagement across the country, according to federal auditors.

The Department of Housing and Urban Development has shortchanged the taxpayers and repeatedly violated federal regulations in its rush to sell groups of surplus properties in Las Vegas, New York and Memphis, the auditors found.

These "bulk sales" are part of HUD's effort to reduce the subsidized properties returned to the government through foreclosure, by offering them in packages to investors.

HUD has taken over thousands of apartments and single-family homes worth hundreds of millions of dollars because it originally insured the mortgages, and this inventory is expensive to maintain. Many units are vacant and abandoned; tenants have remained in some.

The program was run so poorly in Camden that HUD gave mortgages to many welfare recipients who, it is alleged, falsified their applications, including a mortgage issued in the name of a 4-year-old girl. HUD also allowed Camden speculators to resell rundown properties for as much as 20 times the original cost, and many of the houses ended up in foreclosure a second time.

HUD officials have said they hope that the problems were limited to Camden. But the new reports by HUD Inspector General Charles L. Dempsey found that agency officials in other cities reduced sales prices improperly, allowed investors to reap windfall profits and failed to check prospective buyers' credit. According to the audits:

In Las Vegas, HUD broke its own rules by paying more than $200,000 in improper fees to private brokers who had close ties to buyers of the properties. A buyer and broker were brothers; another buyer and broker had the same last name; in a third case, the buyers and brokers were partners in a real estate firm. Another $200,000 in improper fees was paid in three other cities.

In New York, HUD advertised a property for $9,000 when its minimum acceptable price was $40,000. In one sample, two-thirds of the buyers HUD approved ended up in financial trouble. All told, HUD incurred unnecessary losses of more than $1.5 million.

In Memphis, where losses topped $2 million. Nearly half the properties offered in bulk sales were advertised for less than three months, some not at all.

In Camden, some properties were off the market for as long as three years before being offered.

Auditors in Las Vegas found that some investors hit the jackpot at taxpayers' expense. Officials often used the wrong deeds and failed to record bids, the auditors said, and in 67 of 102 cases investigated, HUD did not figure out the best way to sell the properties.

Fay Adams, manager of the Las Vegas office, said he agreed with the audit findings and had doubled the housing sales staff and transferred the official in charge: "I had already started cleaning it up before the auditors came on board."

Adams said he did not check buyers and brokers' relationships -- though HUD is barred from paying a 5 percent broker's fee to anyone close to the buyer -- because "that kind of sleuthing is beyond the office manager's capability."