The District's longest-running comic opera -- The trials and tribulations of the city's hapless election system--may at long last be reaching a finale.

City Council chairman David A. Clarke last week introduced a bill to completely overhaul the troubled Board of Elections and to try to restore some sanity to the city's chaotic voter-registration process.

Whether Clarke's bill will prove to be the answer to the city's problems is uncertain at this point. It has enough elements to guarantee several weeks of political road testing.

But even more of a mystery is why Mayor Marion Barry and members of the City Council have allowed the embarrassment of election day snafus and botched voter registration procedures to drag on for so long.

Barry, campaigning for mayor in 1978, made election reform a major issue.

He had far less to say about the subject last fall, four years after he had assumed responsibility for the elections system. About 20,000 properly registered voters had to cast challenged ballots in the Sept. 14 primary after their names could not be found on the voter roles.

Teddy Filosofos, a Buffalo elections official brought in to manage the city's election system last May, resigned in frustration in October after the primary, grousing about political interference.

He was temporarily replaced by mayoral trouble-shooter David Splitt, who presided over a relatively trouble-free general election and was smart enough not to take the job permanently. As he left, Smith wrote a scathing report calling for immediate action on the festering problems.

Since then Barry has done little to make the election mess a top priority. Nor has he endorsed a plan to remedy the problems, even though some of his aides have laid out options for him.

Barry has dragged his feet on appointing replacements for elections board chairman Albert J. Beveridge III, whose term expired in December, and Virginia Moye, a member whose term expired more than a year ago.

The mayor promised at a news conference last week to make the nominations by the end of this week, although elections officials say they have heard similar promises since the first of the year. Former council chairman Sterling Tucker has been asked if he would serve, but Barry has not sent forward his nomination and there is some opposition on the council to him.

"It'd be like the gambler becoming a preacher," said one elected city official, suggesting Tucker's political fires may not have cooled.

Meanwhile, the lame-duck board has limped along, with the elections general counsel, William Lewis, also filling in as temporary executive director. Lewis has told friends he'll be glad to get rid of the day-to-day responsibility for the elections office.

Other elections employes are demoralized, taking the heat for what really is lack of direction from the top.

Increasingly, citizen groups and frustrated voters are saying Barry must take primary responsibility for the years of neglect of the election system. But there is at least one other, City Council member William R. Spaulding (D-Ward 5), who must share in the blame.

Spaulding has been chairman of the council's Government Operations Committee, which oversees the elections board, for four years yet appears unhurried in finding solutions to the problems.

Spaulding would have been the logical council member to take the lead on the election reform issue but instead left that task to Clarke. Spaulding did sign up as a cosponsor of Clarke's new bill but says that doesn't mean he supports it--a cover-your-bases position that is irritating to some of his colleagues.

It all adds up to a continuing embarrassment for the District, where our local elected government is only 8 years old and the right to vote in federal elections not much older.

Washington, as a majority black city, is particularly aware of historic efforts to keep blacks from voting.

It's been so bad that one black official last year half-jokingly wondered whether the city should get itself included under the federal Voting Rights Act--at least federal marshals could help run the elections.

Other officials have suggested at least there has been no evidence of fraud here.

But with the shape things are in, how would anyone know?