Public officials might want to take careful note of two public admissions of error in the District government last week and the stark contrast they provide to how officials at the University of the District of Columbia dealt with allegations of wrongdoing this summer.

In one case, this newspaper reported early last week that Dr. Andrew D. McBride, the District's public health commissioner, had hired as a consultant a longtime college friend who lives and works in Minnesota and who charged the city for 40-hour workweeks.

McBride called the man, Charles E. Dickerson, more than 200 times from his government car phone in the first six months of this year, sometimes in the wee hours of the morning, running up car phone bills of around $5,000.

When confronted with these reports, David Rivers, director of the Department of Human Services and McBride's boss, responded in several ways.

He ordered an audit of all four car phones used by DHS officials, including his own, and told McBride to stop making long-distance calls. He reviewed the contract file and stated his judgment that the work product was not acceptable and not worth what the city paid for it.

By the end of last week, after back-and-forth negotiations between McBride and Rivers, the two held a news conference at which McBride acknowledged his error and said he will pay back the phone bills as well as the cost of driving his government car to upstate New York to see his children. Dickerson will have to justify his charges or pay back some of his consulting fees, they said.

It can't be much fun to sit in front of television cameras and microphones and admit one's mistakes, but McBride did it, calmly and without expressing bitterness.

He took full responsibility for the contract, which as the contract administrator he should, and he didn't resort to the time-honored excuse that it was all a media plot.

In a second case, D.C. Auditor Otis Troupe discovered belatedly that -- contrary to his original findings -- liens had been paid off on six properties in the Shaw area that Jeffrey N. Cohen is developing under a $12.5 million land deal with the District.

This blew apart Troupe's public accusation, contained in an official auditor's report, that the Shaw deal put city investments at risk and was an example of favoritism to a close friend and political ally of the mayor's, that is, Cohen.

Once shown the documents that contradicted his findings, Troupe didn't waste any time. He acknowledged his error and publicly apologized to Cohen, calling him "blameless" in the matter.

Contrast the way Troupe and the DHS officials dealt with their problems with the way UDC officials chose to respond when The Washington Post started reporting questionable expenditures of UDC President Robert L. Green.

Green was found to have misspent thousands of dollars in university funds for travel, consulting and personal items. Auditor Troupe determined that he should pay back about $13,000.

With the first reports, Green stopped talking to The Post and attacked both the media and Troupe. He refused to provide documents to reporters or Troupe. He suggested that he might sue somebody for libel or slander and said allegations may have been "deliberate attempts . . . to silence the kind of leadership related to bringing change to UDC."

The chairman of the UDC board of trustees, Ronald H. Brown, said before the first story appeared that if Green said his trips were university related, he believed it.

But as more allegations of misspending surfaced, and with the FBI weighing in with an investigation, the controversy continued through the summer. One by one, other persons with responsibility over UDC -- trustees, faculty groups, City Council members -- began demanding more answers.

Finally, many decided it was time for Green to resign, which he did Aug. 23. And at a September City Council hearing, UDC trustees were called upon to explain why they had not exerted more control.

At the health commission and the auditor's office, the officials acted before others decided to act for them, and the quick response helped minimize loss of public confidence.

Of course, the Dickerson matter is not closed. He is supposed to submit another report within 30 days to justify the $38,788 he was paid for seven months of work, and then officials must decide whether they will make him return any money.

Mayor Marion Barry does not defend the Dickerson contract but calls it "an isolated case." The city has regulations 10 times more comprehensive than the federal government's, he argues.

Whether or not that view satisfies critics of city contracting procedures, officials might learn something from Rivers, McBride and Troupe the next time their instinct is to circle the wagons against legitimate public questions.