WITHOUT COMPUTERS, lost ballots or a single missing name on the list of eligible voters, an important election of local leaders has been held that bodes well for the city in the coming year. For the first time in eight years, both the president and vice president of the D.C. school board won reelection. Because these officeholders are chosen by the board members, the process shouldn't be complicated anyway; but for years this annual election has been symbolic of a divisiveness that gnawed at every effort to improve public education in the city.

In the last year, Board President David H. Eaton and Vice President Nathaniel Bush have joined with a responsible majority to lower the board's political profile and raise its level of concentration on matters of direct interest to its clients, the students. That may seem elementary, but it has taken unconscionable amounts of time and a long series of board elections just to establish a civilized atmosphere. So now what?

Money. Mr. Eaton says one priority is to maintain the level of the 1983 school budget. At a time of severe financial pressures on every city agency, this is not likely to be easy -- nor should it be. Not only should spending requests be subject to thorough justification, they also should be accompanied by some recognition in the budget that more money is not the sole answer to educational shortcomings. For starters, there is the job of leasing, selling and rearranging unused school space and grounds.

Teaching. This is the year to concentrate on a solid teacher evaluation system, to measure and reward the inspiring classroom educator and to make the case fairly and firmly against those whose performances do not measure up. Already, Superintendent Floretta McKenzie has improved working relationships with the teachers and their union, and a joint report on teacher evaluation procedures is due soon. The school board should seize this critical opportunity to raise classroom standards, parental expectations, teacher morale and student test scores.

Curriculum. The "back-to-basics" emphasis, welcome as it has been, should not have to result in the elimination or dilution of foreign-language, music and art instruction. These are not "frillc"; on the contrary, they should be "basic" to the elementary as well as high school classroom fare.

Policy-making. While the city's charter and other laws vest authority over school policies with the board, and not the mayor or council, this should not be interpreted as a reason to resist all overtures from the mayor to increase cooperation between city hall and the school board. In addition to decisions on what to do with space, there are other purchasing, building-and-grounds and logistical decisions that are best made with joint participation. Certainly the board should resist any attempts at unnecessary usurpation of its powers by Mayor Barry; and so far, thanks to Mr. Eaton, Mrs. McKenzie and the board majority, the relationship with city hall has been marked by good sense instead of by the bitter resentments of earlier years.

There are definite signs of improvement in the schools, most notably in the test scores of the younger students. Washington can't afford to lose this precious momentum--and therein lies the greatest challenge for the school board throughout 1983, and beyond.