Carol Schwartz is running for mayor and her candidacy should make the contest a far better one. We say this not as an endorsement but because until now there really wasn't a contest. As we noted a month ago, Mayor Barry has been sailing toward November without any well-known opponent to jab at the weaknesses of his administration or to propose new approaches to government. Mrs. Schwartz fills that bill. She has been a member of the school board and has run at-large as a Republican to capture a seat on the D.C. Council. She has the recognition, the credentials and the competitive spirit to give Mayor Barry the challenge he deserves. If the result of this competition is a serious debate about the accomplishments as well as shortcomings of city hall, Washington's voters will be well served.

Mrs. Schwartz wasted no time yesterday pointing up some of the issues she intends to raise in seeking the Republican nomination in September and election in November: "housing, our neglected neighborhoods, the homeless, prisons, youth affairs . . ." She noted that these are not "racial or partisan issues -- they are people issues." What Mrs. Schwartz would do about them remains to unfold in detail -- but then so does what Mr. Barry would do. The mayor says he intends to talk openly and often about the issues that he has not been able to resolve to his satisfaction -- and to propose solutions. That can't hurt, and neither can some constructive sparring by an energetic challenger.

The campaign should focus on those in this city who do not enjoy the most effective means of making their complaints known -- those who live in substandard housing or on the streets or behind bars. It should focus also on the matter of public trust, which Mr. Barry already is raising in his campaign appearances.

Anyone familiar with Mayor Barry's political style knows that he, too, can be a vigorous competitor, that he relishes a good contest. But until the entry of Mrs. Schwartz, the greatest threat to Mr. Barry was complacency. Says Mrs. Schwartz, "If people want four more years of him, let them have him." For his part, Mr. Barry has been saying all along, "I'm looking for competition. I welcome it." Now he has it, along with the keener attention of Washington's electorate.