When it looked as if District Mayor Marion Barry was in political trouble three years ago, 10 other Democrats and Republicans, including Patricia Roberts Harris and nearly a third of the City Council, scrambled to challenge him. After all, there are few elective posts to run for in the District, and no other so important or attractive as the mayor's office.

But the usual cluttered field may not be evident in next year's race, as Barry continues to tighten his grip on the office and many of his potential challengers already are beginning to take themselves out of the race or are looking beyond it to 1990.

All four City Council members who challenged Barry last time around seem wary about making a run in 1986. John Ray (D-At Large) says flatly he won't run next year. Charlene Drew Jarvis (D-Ward 4) says it is too early to speculate on her plans; some of her colleagues believe she intends to challenge council Chairman David A. Clarke instead.

John A. Wilson (D-Ward 2) last week ticked off a laundry list of issues he could raise against Barry in a rematch next year, but he conceded, "I don't think a majority of the people think I'm ready to be mayor." And Betty Ann Kane (D-At Large), who spent two years paying off a $50,000 debt from her aborted 1982 mayoral campaign, said she hasn't made a decision but indicated it would take a dramatic turn of events to get her to run next year.

Outside the council chambers, Republican Vincent E. Reed, a former D.C. school superintendent and now an executive with The Washington Post, has told local business people and activists who have urged him to run that he's not interested.

The potential challengers who would speak for the record share a common concern: money.

"The major barrier is financial," Kane said. "It's difficult to raise money to run against the incumbent. An incumbent is formidable, and the longer they're in, the more they have at their command."

Barry amassed a $1.3 million campaign war chest in 1982, a record for a District race, while Harris, a prominent Carter administration official who died this year, and others struggled to keep their campaign organizations afloat. Kane and Wilson dropped out before the election because of fund-raising difficulties.

Barry won the all-important Democratic mayoral primary that year with 59 percent of the vote, sweeping every area of the city except Ward 3, a predominantly white, middle-class area west of Rock Creek Park. Last December, a Washington Post survey showed that 65 percent of D.C. residents believed that Barry was doing a good or excellent job as mayor.

Last week, Barry said that his plans for a third term were "evolving" and that he hasn't made a final decision about whether to run. But many D.C. Democrats assume that Barry has begun campaigning for another four-year term and that, if need be, he could double his fund-raising effort of three years ago.

The mayor recently stepped up his public appearances, including carefully orchestrated "town meetings" in each of the city's eight wards to highlight his accomplishments. He has ordered the police to wage yet another offensive against drug dealers in the Shaw community. And he asked the City Council to put additional funds into this year's budget to fix up the District's dilapidated public housing projects.

This summer, Barry and his aides will begin announcing $30 million worth of job-producing economic development projects. Some council members predict that by the time Barry officially kicks off his reelection campaign, the District's 30,000-member bureaucracy will be humming and the mayor's citywide political organization will be running in high gear.

"I think he's weathered his political storms, and unless something very, very dramatic happens between now and then, I think he'll be reelected by a very sizable plurality," said City Council member Frank Smith Jr. (D-Ward 1), a Barry ally.

One of those storms stemmed from reports that Barry had testified in January 1984 before a federal grand jury that was investigating drug use by D.C. government employes and others.

Barry said publicly that on a number of occasions, through late 1982, he had visited the 16th Street NW apartment of city employe Karen K. Johnson, who later was convicted of selling cocaine. The mayor said he sipped cognac and champagne with Johnson, but he denied that he ever purchased or used drugs. Last April, after the grand jury had concluded its investigation, Barry blamed the press for attempting to ruin his political career by linking him to Johnson.

There have been other problems. A federal grand jury is investigating whether Ivanhoe Donaldson, Barry's longtime friend and political adviser, misused city funds while serving as director of the D.C. Department of Employment Services and as deputy mayor for economic development. Also, a grand jury is continuing to probe alleged wrongdoing in the city-sponsored Bates Street housing redevelopment, which was once the showcase of Barry's housing program.

Last month, Barry fired Jose Gutierrez from city government after the mayor's legal counsel issued a report alleging that Gutierrez had steered "lucrative, give-away contracts" and leases to acquaintances while he headed the D.C. Department of Administrative Services. Gutierrez responded by filing suit in D.C. Superior Court, seeking $3 million in damages and claiming that Barry and City Administrator Thomas Downs had tried to force him to grant contracts to the mayor's political cronies.

Also last month, it was discovered that Assistant D.C. Treasurer Fred Williams submitted a backdated memorandum to a City Council committee in an effort to justify the city's decision last December to begin investing with a New Jersey-based securities firm that later went bankrupt.

A source familiar with Barry's thinking said last week that the mayor is confident that most voters believe he has done a good job as mayor and will not be influenced in their thinking by reports of government scandal or suspected wrongdoing.

At his town meetings, the mayor rarely is asked to respond to reports of problems within his administration. At one such session in Ward 5 recently, residents were mostly concerned about getting their alleys and streets cleaned and removing broken glass from a neighborhood schoolyard.

"The public has a short memory for the bad as well as for the good," the source said last week.

Council member Kane said that the Barry administration's awarding of contracts is ripe for attack in next year's campaign, but only if his opponents can demonstrate to voters that abuses of the contracting process adversely affect the services they receive.

"There is a sense that something is not right," Kane said. "The challenge for someone running is to put that together, to make the connection."

Wilson contends that the mayor is vulnerable, as well, in his handling of city finances and budgetary matters. Wilson, chairman of the council's Finance and Revenue Committee, spearheaded a review of the District's investments with the now-failed Bevill, Bresler & Schulman Inc. that uncovered problems with the city's cash management practices.

Wilson said he wants to be mayor someday but suspects he may have to sit out the 1986 race unless lightning somehow strikes.

"I think the amount of money Barry could raise is unlimited," said Wilson. "When you have the kind of financial support he has, it is very difficult to get people to gamble with someone like Wilson who has not run at-large.