The Metro transit authority has entered its final weeks of labor negotiations with the Washington area's largest transit union, amid mounting concern about Metro's rising deficits and signs of unrest among transit workers.

The volatility of the talks was underscored in the past few days when a dispute about work schedules in a maintenance shop led to warnings of a possible strike by the union. The disagreement was temporarily settled at a hurriedly scheduled meeting between Metro and union officials, and it is expected to be discussed further during negotiations over a new contract.

Strikes are barred under the current three-year contract between Metro and Local 689 of the Amalgamated Transit Union, which is set to expire April 30. The agreement also provides for binding arbitration if an impasse is declared in the negotiations. Nevertheless, wildcat strikes have repeatedly occurred, including a seven-day walkout that crippled bus and subway service in July 1978.

Metro officials have portrayed the negotiations as central to their efforts to hold down skyrocketing costs for bus and subway service. Metro's deficits, which must be offset by tax revenues from Washington-area governments, have climbed steadily in the past 10 years and are expected to exceed $200 million in the next fiscal year. Wages and benefits paid to unionized employes account for almost 60 percent of local transit costs, Metro officials say.

"We don't want this to go the way of General Motors and Detroit to the extent that too good of a deal kills the cow," said Prince George's County Councilman Richard J. Castaldi, chairman of Metro's board of directors.

The union, while indicating flexibility about what it considers relatively minor issues, does not appear prepared to offer any major concessions to the transit system's management on wages or fringe benefits. Union leaders reject Metro officials' complaints and accuse the transit authority of mismanagement, including failure to stem recent declines in the number of passengers who ride Metro buses and trains.

"If you're talking about giving in or giving back, then you're talking about electing another president three years from now," said James M. Thomas, who was recently elected to a three-year term as president of Local 689.

In recent years, transit strikes have troubled major cities from Boston to Los Angeles, including a protracted walkout that ended last week by employes of the Metro-North Railroad, a commuter system in the New York City area.

Although neither Metro nor the union has publicly spelled out its bargaining aims, officials said key issues include wages, a long-controversial cost-of-living clause that ties employes' pay to changes in the Consumer Price Index, and a series of complex employment practices that provide premium pay for special work schedules and assignments.

The negotiations have been closely watched by District of Columbia, Maryland and Virginia officials and by local labor leaders because of the transit union's size and the impact any settlement will have on public spending. Local 689 represents nearly 5,500 bus drivers, subway operators, mechanics and other employes.

Its contracts normally set a pattern for agreements between Metro and Teamsters Local 922, which represents another 250 Metro bus employes. The local Teamsters' contract with Metro also will expire April 30.

Prospects in the talks are uncertain, partly because of shifts in union and Metro negotiators since the last contract was signed. Thomas, who was elected in December, is the first black official to head the transit workers' local.

Metro's chief negotiator is Gayland K. Moffat, who was hired recently after gaining a reputation as a tough labor-relations strategist for the Utah Transit Authority in Salt Lake City.

According to union and management officials in Utah, Moffat played a key role in a bitter labor dispute in 1981, during which the authority locked out its 400 unionized employes for four days. The dispute led to a wage freeze. Later, a controversial cost-of-living adjustment clause was eliminated from the union's contract. Moffat, 32, was hired in January as Metro's human resources director at a salary of $63,603 a year.

Thomas, 42, a former bus driver and union recording secretary, took over as president of the predominantly black local after overwhelmingly defeating four other candidates in union elections. Previous leaders have been accused of losing touch with union members.

Thomas, who is paid $55,638 a year, is described by local labor leaders as likely to prove more aggressive than his predecessors and to establish closer ties with rank-and-file workers.

The negotiations began shortly after Metro employes became the first union members in the Washington area to have their pay reduced--by about 5 cents an hour--as a result of decreases in the Consumer Price Index.

During earlier years of double-digit inflation, Metro workers received cost-of-living raises ranging as high as 18 percent annually, and the cost-of-living clause was regarded as a plum for the union. In November and December of last year, however, the CPI dropped.

For Metro employes, this downturn was reflected in paychecks starting in February. Veteran bus and subway operators had their wages cut by a nickel to $11.94 1/2 an hour.

Though this was the first cost-of-living reduction in the Washington area, several major unions have reported similar decreases for workers elsewhere in the country as a result of the CPI decline.

The United Auto Workers said hourly wages were cut by a penny in March because of a cost-of-living decrease, and the United Steelworkers of America reported a cost-of-living reduction of 3 cents an hour in February.

The nickel-an-hour cost-of-living decrease caught many Metro employes by surprise, and it led to a crowded meeting of union members, marked by confusion and complaints.

Thomas said later, however, that most members had reluctantly accepted the cost-of-living cut as unavoidable, and he cited the decrease as evidence of the fairness of key contract provisions.

"That's one of the reasons we like the cost-of-living clause," he said. "If it stays down, we're willing to stay down."

Metro officials, who have repeatedly objected to the current contract's cost-of-living provisions, hailed the decrease, saying it could save the transit agency $750,000 annually.