D.C. City Council member John A. Wilson, a one-time civil rights activist with a penchant for audacious rhetoric, formally entered the race for mayor yesterday, criticizing Mayor Marion Barry's administration as gloomy and crisis-oriented.

Wilson, 38, a member of the council for seven years and chairman of its Finance and Revenue Committee, promised to restore public confidence in the government, particularly in its handling of the budget, and to make city residents proud of being Washingtonians.

"The credibility of the administration itself has caused a great deal of problems," Wilson said in an interview preceding his campaign's kickoff. "They tend not to know what's going on in their own government."

Wilson (D-Ward 2), who actively supported Barry's candidacy in 1978, said that he now is challenging his one-time ally and fellow civil rights activist because the mayor's administration "has bum-fumbled as badly as the previous administration."

Meanwhile, council member Betty Ann Kane (D-At Large) formally announced her campaign for mayor to more than 100 cheering supporters at her newly opened campaign headquarters on Connecticut Avenue, while balloons floated in the air and a jazz band played outside.

Kane said she is "sick and tired" of an administration that she said does not efficiently provide basic city services.

"Every year, I have heard the head of the water department promise to straighten out the water bill mess," she said. "The water bills are just one typical situation.

"I could use the example of the potholes, or late unemployment checks, or the clerk who's always out to lunch and can't answer your question . . . . For every frustration there is an explanation: We need more staff, more money, more authority, the check is in the mail . . . just excuses."

There were no balloons or brass bands at Wilson's announcement. He shunned much of the traditional hoopla and instead spent most of the day knocking on doors throughout the city, accompanied by a small band of eight campaign workers.

In mounting their campaigns, Kane and Wilson both have borrowed a page from Barry's own successful 1978 campaign strategy, in which Barry repeatedly accused then incumbent Walter E. Washington's administration of "bumbling and bungling."

Wilson said that he intends to hit hard at Barry for failing accurately to forecast city revenues and for spending and waffling on major issues. Wilson said he is personally angry with the mayor for first supporting and then abandoning gasoline and inheritance tax proposals that the mayor had asked Wilson to shepherd through the council.

Wilson said he also is disappointed in the mayor for taking the city on a fiscal rollercoaster ride during the past three years, during which estimates of the city's accumulated deficit constantly changed.

"We don't know whether we've eliminated part of the deficit, because the administration can't tell us what bills have been paid," said Wilson.

As he knocked on doors yesterday, Wilson urged city residents--some of whom had only a vague notion of who he was--to keep an open mind.

"The city at this point needs new leadership and needs to be a little more aggressive," Wilson told Earl Bell, a retired government employe on Blaine Street NE. "We think the city can be improved without increasing taxes. We need to streamline the bureaucracy . . . . I hope you will at least consider me."

Wilson has been successful in his early fund-raising efforts and has collected nearly $100,000. Still, he acknowledged in an interview last week that he is having trouble convincing businessmen and political insiders that he is a serious candidate who is in the race to stay.

"I stay awake at night wondering why nobody takes me seriously," Wilson said, only half joking. "I'm as serious as a heart attack about running."

Some observers feel that in order to win, Wilson first must overcome his reputation for madcap humor and brutally frank political comments, just as Barry in 1978 had to allay middle-class voters' concerns about his past days as a black activist.

Last November, for instance, after the council reversed itself and voted to kill a bill to discourage real estate speculation, Wilson publicly accused some of the members of having sold their votes to area real estate investors and home builders.

A few weeks later, during heated discussion of a redistricting plan that would shift most of Georgetown from Ward 3 to Ward 2, Wilson declared: "I don't want the people of Georgetown in my district . . . . I don't think the majority of people in my district want them."

Later, after Georgetown had been moved into his ward, Wilson pooh-poohed his own statement as pure political hyperbole. Wilson insisted he had nothing against Georgetown residents. His statement merely had been a sop to some of the poor residents of his ward, who feel they have nothing in common with Georgetown residents.

"People say I'm erratic, but it's just that I like to win, and I use everything at my disposal to win," he said. "If that means I holler or gesture or raise my voice, then I do it."

One prominent D.C. businessman, who supports Barry, summed up the concerns about Wilson this way: "People like John, but the thing is, do they really want him for mayor? I don't know if he is ready. Now as City Council chairman, I think he'd be a winner. But John is too unpredictable for me to feel comfortable with as mayor ."

Although Wilson claims that a poll he commissioned shows him with surprising support in several key wards, so far the most tangible sign of his strength has come in last month's campaign finance reports, which indicated that he had raised $96,048.

Wilson said that he plans to spend about $58,000 this month on television and radio advertising to improve his name identification and to review his record, including his sponsorship of laws affecting condominium conversion, consumer protection and gun control. However, he said, he has no plans to try to dramatically alter his public image.

"Too many politicians are simply clones of media consultants," Wilson said. "I'm not going to change. I like what I am."

Born in Baltimore and raised on the Eastern Shore of Maryland, Wilson is a former member of the Student Non-Violent Coordinating Committee and a one-time anti-Vietnam War activist who once was a roommate of Ivanhoe Donaldson, Mayor Barry's chief political adviser. Wilson helped run Walter E. Fauntroy's successful campaign for nonvoting delegate in 1971, and first was elected to the City Council in 1974. He was reelected in 1976 and again in 1980.

When Barry left the council in 1979 to become mayor, Wilson, who had served as head of the council's committee on consumer affairs, replaced Barry as chairman of the finance committeee, which has jurisdiction over city tax laws.

He is married to the former Bonnie Biro and lives near 18th and Q streets NW, near Dupont Circle.

While Wilson did well in the first round of fund-raising, Kane fared poorly, raising only $24,860 as of the end of January. In announcing her candidacy yesterday, Kane told her supporters that she will be asking for money as well as support during the race.

Kane's fund-raising problems are partly due to her strategy of delaying requests for contributions until her campaign has gained sufficient momentum to remove all doubts that she is running for mayor and that she has a chance to win.

"Wait until March," said former D.C. Corporation Counsel John R. Risher Jr., a key Kane supporter, referring to the March 10 financial report candidates are scheduled to file.

"We are going to be more aggressive about money from this day forward," Risher said. "But I don't think it's going to take as much money as some people say. It took a lot of money to build the Edsel, and we are not building an Edsel."

With Wilson, Kane, and council member John L. Ray (D-At Large) now formally in the race and Barry expected to announce soon, former City Council chairman Sterling Tucker and Patricia R. Harris, a former Carter administration cabinet member, are the only major potential candidates whose plans still are uncertain.