Secretary of Energy James B. Edwards, the only southern dentist in the Reagan Cabinet, has told the White House that he will accept the presidency of the Medical University of South Carolina.

Edwards is scheduled to depart June 30 and thus will become the first Cabinet member to leave the Reagan administration.

He will leave to mixed reviews.

The former governor of South Carolina, whose memorable comment when he returned to dentistry was that he wanted to "get my hands in the saliva again," came in with the expectation of closing down the department, as Reagan had promised in the 1980 presidential campaign.

Instead, he became a defender of some of Energy's embedded giveaways, notably the synthetic fuels program that Edwards saved from decimation at the hands of budget director David A. Stockman last year.

Now that the talk of doing away with the Energy Department by merging it with Commerce has become a paper promise, the administration is seeking an energy expert to replace Edwards.

"We want someone who will run the department aggressively," an administration official said last week.

Stockman lost another intra-administration battle last week over whether President Reagan should embrace a Republican congressional proposal calling for $40 billion of Social Security savings over the next three years. Stockman argued for caps on cost-of-living increases in Social Security, a position John B. Connally also apparently supported during a lunch with Reagan.

But the overwhelming view in the White House, led by chief of staff James A. Baker III, was that Reagan should leave the "savings" unspecified, pending a year-end report by a commission headed by Alan Greenspan.

This is what Reagan tried to do in the Rose Garden the next day.

Even with this hedge, however, the president has given his opposition an opening on an issue to which his polls say he is especially vulnerable.

Since Reagan won't and can't specify where the savings will come from, Democrats are free to accuse him of trying to slash Social Security benefits even though the commission may not recommend any such thing.

Win or lose, Stockman is staying in the Cabinet for the duration of the budget battle, say high administration officials, who also put down a spate of other resignation rumors. Included are the rumored departures of Deputy Defense Secretary Frank C. Carlucci to a New York bank and Commerce Secretary Malcolm Baldrige to anywhere. All of these denials are hedged by the time frame of the November elections.

Reagan's longtime personal assistant, Helene A. von Damm, who was in line to become ambassador to her native Austria, will stay at the White House and take over the presidential office of personnel when E. Pendleton James departs in June.

Von Damm, who technically holds the No. 2 personnel post but in effect has been in charge of the operation for several months, is credited with improving the White House appointments process.

The MX is back, at least for a while.

A compromise engineered by Tom Reed, defense specialist of the National Security Council, has resulted in a commitment by Senate Majority Leader Howard A. Baker Jr. (R-Tenn.) and Senate Armed Services Committee Chairman John G. Tower (R-Tex.) to restore $800 million for the orphan missile, which the administration wants in time for upcoming strategic arms reductions talks.

The White House commitment is to agree by Dec. 1 on a permanent basing system and to scrap the idea of using MX missiles in airplanes on continuous patrol, a plan that captivated Secretary of Defense Caspar W. Weinberger and repelled Tower and other Senate defense specialists.

Veterans Administration Director Robert P. Nimmo, under fire for spending $46,000 on his offices and giving $6,900 worth of the used furniture to his daughter, Commerce Department Director of Public Affairs Mary Nimmo, has earned a reputation as "the best-tanned member of the administration." The description refers to Nimmo's proclivity for scheduling speaking appearances that coincide with opportunities to improve his golf game.

The White House counteroffensive against the CBS documentary, "People Like Us," has ended inconclusively.

White House communications director David R. Gergen, architect of the response, believes that it "put the media on notice that when there is something unfair we're going to respond to it, so people will be more careful next time."

The other view is that the White House unwisely widened the audience of the biting critique of Reagan policies that was seen by only a small percentage of viewers.

Richard Darman, who wanted the administration to counterattack on the fairness issue without making reference to CBS, compared the strategy with that of former Virginia senator William Scott, who called a press conference to rebut a magazine report that had declared him the least intelligent member of the Senate.