D.C. Mayor Marion Barry easily won renomination for a second term yesterday as Democratic voters gave strong support to all but one of the city's incumbents, City Council Chairman Arrington Dixon, who was ousted by Ward 1 council member David A. Clarke.

The city's election was marred again by widespread problems, similar to those that have plagued its voters for years. About 17 percent of the voters who showed up at the polls were not listed as registered voters and were forced to cast challenge ballots that will not be counted for another week, according to election officlas. The voting snafus were exacerbated by a strong voter turnout, they said.

D.C. voters also overwhelmingly approved an initiative to require judges to impose mandatory minimum sentences for persons convicted of committing violent crimes while armed with handguns, or selling illegal drugs.

Barry, a 46-year-old former civil rights activist, issued a statement claiming victory in the hard-fought four-way mayoral race about 10:30 last night, moments after his chief rival, former Carter cabinet official Patricia Roberts Harris, conceded the election.

In his victory statement, Barry described the election results as a reaffirmation of the goals of his administration, although he conceded that his three opponents had raised legitimate criticisms.

"Many spoke with a clear voice about what remains to be done," he said. "Already, even as we celebrate and congratulate, I have directed my cabinet to review those areas in which we can do more, and to develop plans for improvements which will be implemented in our second term."

Barry praised Harris and his two other challengers, City Council members Charlene Drew Jarvis (D-Ward 4) and John Ray (D-At Large) for running good campaigns, and urged them "to join me as we move forward together, to enhance the quality of life for all the citizens of the District.

"The tasks and choices ahead are not easy ones," the mayor added. "In an era of less -- less federal support, less economic well-being, less consensus on the need for compassionate government action that leads to genuine equality for all--we will have to do more."

With all 137 precincts reporting, Barry had 56,638 votes to 33,282 for Harris, 3,266 for Ray and 2,711 for Jarvis.

Early this morning, the D.C. Board of Elections and Ethics said it had counted the ballots of 101,283 voters, but said that another 20,000 challenge ballots were cast, which won't be counted for up to a week. The election results will not be official until those votes are counted, but the counting of such ballots has seldom altered the outcome of election results in past D.C. elections.

Harris appeared before her supporters at the Hotel Washington downtown shortly after 10:15 to announce that she had just called Barry to congratulate him. Some expressed loud disappointment.

But, she told the crowd, "The people have spoken."

"I've campaigned all over this city," she said, "taking my case, my vision and my hope for a great vision for the city to the people of the District of Columbia."

She said she had raised important issues during the campaign and proposed important solutions.

"I congratulate Mayor Barry for running a very effective campaign. I wish him well," she said.

After thanking those who voted for her, she pledged to them, "Your labors on my behalf will never be forgotten."

Barry, a former school board and City Council member, could become the District's first mayor to serve to serve two elected terms if he wins the general election Nov. 2. He became the city's second elected mayor in 1978, succeeding Walter E. Washington.

E. Brooke Lee, a real estate agent and member of the politically oriented Lee family of Maryland, won the Republican mayoral nomination, 2,497 to 1,585 for James E. Champagne, a speech writer.

Clarke, 38, a lawyer who now heads the council's Judiciary Committee, is also a former civil rights activist. He has no opposition in the general election and will become the first white to serve as chairman of an elected city council in the District, where blacks comprise 70 percent of the population.

"I am extrememly happy and looking forward to working with my colleagues on the council and giving them solid leadership with the mandate the people have given me," Clarke said enroute to his victory party.

Clarke initally pulled out of the council chairman's race because he said private polls indicted that a white could not win the seat. But he later reentered the race and made a strong surge in the polls in the final weeks of the campaign.

The mayor's strong campaign organization privately encouraged Clarke and many of the mayor's workers also supported Clarke. Barry's campaign workers handed out literature for Clarke yesterday at many of the city's polling places.

With all precincts reporting, Clarke defeated former City Council Chairman Sterling Tucker and incumbent Dixon. Clarke received 40,702 votes to 25,950 for Dixon and 24,555 for Tucker.

Betty Ann Kane, a Democratic at-large member of the council, also won a convincing reelection victory over school board member Barbara Lett Simmons and congressional aide Johnny Barnes.

D.C. Del. Walter E. Fauntroy, an 11-year House veteran, won easy renomination. He did not have a challenger on the ballot, but faced a write-in campaign from a former Barry aide, Marie Dias Bembery.

Although about one of every five voters going to the polls yesterday had to cast a challenge ballot, none of the major candidates said last night that they would immediately challenge the election results in court.

"Given the history of problems with elections," Harris told a reporter, "this is a matter between the voters of the District of Columbia and their government."

Frank Smith, a Ward 1 school board member, apparently won the Democratic nomination to replace Clarke as the ward's City Council representative, though his closest challenger, housing activist Marie S. Nahikian, said she will contest the outcome.

Three other incumbents, Polly Shackleton (D-Ward 3), William R. Spaulding (D-Ward 5) and Nadine P. Winter (D-Ward 6) won their renomination bids to new four-year terms.

As election day dawned with misty skies and warm weather, long lines formed at polling places before they opened at 7 a.m. Throughout the day, the heavy turnout continued in most areas of the city, according to precinct captains.

As they reached the entrance to polling places, voters had to run a gamut of campaign workers dressed in a kaleidoscope of colorful hats and shirts and carrying signs for their candidates. At some polling places, the candidates' supporters set up tables, ate fried chicken and fruit pies and occasionally offered voters some of the food, along with the ever-present campaign leaflets.

Inside the precints, thousands of voters whose names were not on the official voting rolls were forced to line up throughout the day at tables where they were asked to sign affidavits asserting that they were registered to vote.

Among the major candidates, Barry's election-day operation appeared to be the best organized. In Ward 6, his workers brought in elderly people by the busload. When election officials asked the names of some of them, several replied: "I just want to vote for Marion Barry."

The race for mayor marked a coming of age for D.C. politics.

For the first time, an incumbent mayor used the full panoply of his budget, appointment and service delivery powers to win the support of public employe unions, community organizations and special interest groups.

Campaign contributions became a critical barometer of political viability. The four Democratic candidates who finished the race spent a record $2 million, with Barry alone raising more than $1 million.

Two mayoral candidates, City Council members John A. Wilson (D-Ward 2) and Betty Ann Kane (D-At Large), dropped out because of shortages of funds.

Finally, the large and impressive field of candidates, including Harris, a nationally prominent public administrator, diplomat, educator and former cabinet secretary, underscored the growing stature of the office of mayor in post-home rule Washington.

But the bulging field, which at one point totaled eight Democratic and two Republican candidates, also was indicative of the widely held belief that Barry was politically vulnerable going into the election year.

Barry's administration had been marred by three years of budget crises, bureaucratic snafus, limited success in keeping his 1978 campaign pledges, and minor scandals.

Many of his challengers assumed there was widespread disenchantment among voters who felt Barry hadn't lived up to his pledge to end "bumbling and bungling" in the city bureaucracy or who felt he lacked the character or vision to lead the city to greatness.

Harris formally entered the race April 3, and quickly established herself as Barry's chief challenger with a strong showing in early polls and by demonstrating fundraising capabilities.

The late start was costly, however. Harris had to start campaigning from scratch and had difficulty in the late stages matching Barry in organization and get-out-the vote efforts. By attracting attention, she quickly became a target of the other candidates. And Harris also encountered difficulty identifying a political base.

Barry proved to be a tough campaigner and crafty politician. He tailored his 1982 and 1983 budgets to highlight housing starts and road paving and street repair efforts and increased spending for various special interest groups.

He parceled out appointments to city boards and commissions to improve his standing among women, gays and Hispanics.