SHARI B. KHARASCH is quitting her job in the manner to which the Board of Elections and Ethics is accustomed to doing things: slowly. She wants to stay on as head of the three-member board until Dec. 15, which means through the general election next month. In theory, she should go right away, but with only four weeks and a matter of days until that election, the timing of her departure should not be the central issue. The next mayor should name a successor - someone with solid administrative experience.

Right now, the impending election is the most important business, and preparing for the vote count should get top priority. We think the boar d should try hand-counting the ballots in the precincts, and we are far from alone in this. Many elections experts have cited the old-fashioned hand count as reasonable way to do things in the absence of reliable voting machines. Richard M. Scammon, for one, notes that all around the world, where machines aren't used and ballots are reasonably short, the efficient method is a hand count in the precincts. And in the District, there are many talented people in those precincts who know a little something about elections and whose organizations - such as the D.C. League of Women Voters - could assist in the counting.

But no, the board officials continue to line up vote-counting gadgets for one ward while planning for the rest of the ballots to be handled in another round of computerized madness at a central tallying point. What degree of trust should community place in their judgment? To ask the question is to answer it.

We think Mayor Washington, the city's chief executive should do everything legally possible to see to it that the next election goes smoothly - and he could begin today by asking the semi-autonomous board to try a hand count in the precincts.