AT LAST, from the District Building's point of slow returns, there is a complete vote count and it shows what the running count did: that Marion Barry won. And no evidence of fraud, tempering or any gross inaccuracy that would necessitate a new election has been produced. It was a matter of getting it all counted - and it happens to be largely thanks to a worker for Mr. Barry, Philip Ogilvie - that failures were cited and corrected as the process went along.

So now perhaps the District can move on to the next phase, which is the general election on Nov. 7. And although election officials may think it's rushing things a bit to talk about what they are going to do or not do about counting that next vote, there are some changes that should be considered right away.It isnt that the system is unorganized; it is disorganized, with all sorts of elaborate logistics that can - and do - gum up the works. What we suggest is a little zero-base thinking, if you will, a back-to-basics plan for counting ballots.

Instead of hauling all the ballots to a central mad-house, let's have a good old-fashioned election, as in the days before computers - with hand-counting done in the precincts. The District has had enough disasters tinkering with punch-card voting, centralized counting and computer or semi-automated counting and tabulating of ballots that may or may not be marked with the right kind of pen or pensil. Until the basics of election administration are mastered, people and hand-counting are preferable to breakdowns and buck-passing.

True, counting in the precincts requires many people. But, for the most part, they are in place at the precincts already, and many of them are neighborhood residents who have a strong interest in getting correct results promptly. That has got to be better than relying on high school students new to the job, which is what officials did this last time. We're all for giving students work then possible, but this is serious business; there are many other talented people in the precincts who would welcome the opportunity to do a first-rate, efficient job as much as they would welcome the job itself. Surely, too, the D.C. League of Women Voters and other experienced organizations could be brought in to assist; and the counting could be done in the presence of poll-watchers for the parties or the candidates, with a precinct captain and roving supervisors. Once the out-loud counting has been completed, the results could telephoned to the elections board and the ballots sealed for official delivery by a supervisor along with, say, representatives of opposing candidates.

The business-as-usual bureaucrats may argue that it's too late, that it's too much to do, that it's too expensive, too different or too likely to produce new foul-ups. But the old system worked pretty well around the country for quite a few elections. And if Mayor Washington would like to give his constituents a farewell present to remember, he should do everything legally possible to see to it that the election goes smoothly this next time out.