Joseph P. Yeldell, a Democratic candidate for D.C. delegate, sees himself as a mediator of disputes, a resolver of problems and fixer of whatever is wrong. Although he has never held elective office, he behaves like a politician, talks like a ward healer and seems to know everybody.

"Mr. Fix-It," as Yeldell is known, greeted potential voters at nursing homes and bus stops last week, calling women "sweetie" and men "buddy." When commuters told him they lived in Maryland, he pressed literature into their hands anyway and told them to tell their District friends about his campaign. Yeldell, 57, a longtime District official, lost in his only other bid for office. In 1971, he left a seat on the old appointed D.C. council to run for the nonvoting House seat. He lost to his high school friend, Walter E. Fauntroy.

Nineteen years later, Yeldell is again trying for the same seat, now being vacated by Fauntroy after nine terms. And Yeldell is stressing his extensive experience as a District official.

During the administration of Mayor Walter E. Washington, Yeldell headed the Department of Human Resources between 1971 and 1976. He served as general assistant to Washington in 1977 and 1978.

His career was interrupted in 1978, when he and real estate developer Dominic F. Antonelli were tried and convicted in federal court on charges that Antonelli had bribed Yeldell with a secret $33,000 loan in exchange for a $5.6 million government building lease.

The conviction was thrown out after it was discovered that one of the jurors had failed to reveal that her father had been fired by one of Antonelli's companies 10 years before. Both men were acquitted in a second trial conducted in Philadelphia in 1979.

At a forum last week in Mount Pleasant, Yeldell bristled when questioned about his conviction.

"I have never been found guilty of any crime," he shot back.

Yeldell made a comeback during Mayor Marion Barry's administration, beginning with a job as special assistant to the city administrator in 1979. In 1983, Yeldell became director of the Office of Emergency Preparedness, a job he held until last May, when he announced his candidacy for delegate.

Yeldell still sounds like the office director when he greets District residents. Last week, he promised the owner of a privately run facility for former St. Elizabeths mental patients that he would resolve problems with building inspectors. Later, he told a restaurant owner he would see about getting better police protection of the establishment.

"I am the consumate team player," Yeldell said. "We have to go to Congress with a united face. The delegate is an extension of the District government."

Yeldell says the work of the delegate is to coordinate congressional oversight of District legislation. He sees the job as that of an ombudsman, introducing members of Congress to the city and encouraging the federal government to use the District as a laboratory for new programs.

Yeldell said at least one member of Congress has already seen him in the liaison role. He said a senator called his office last year to complain that his car had been towed on a Friday night and that he wouldn't be able to claim it until the following Monday.

"I called the head of the impoundment section and he got a man down there to open the gate," Yeldell said. "Some folks may object, some may say that is special treatment. But we have to recognize power. We have to give those people some perks."