By 8 a.m. on Monday, the line of over 100 people snaked out from the Petworth branch of the unemployment office down Kansas Avenue and onto Georgia Avenue. The line was full of grumbling frustrated people complaining that they had not received an unemployment check for as many as six weeks -- or since the District began a new system of handling unemployment checks because the old system was so inefficient.

Two weeks ago 26 paramedics working for the city were demoted because of a bureaucratic error that had mistakenly promoted them and given them raises of as much as $4,000. And a few months agon, the city sent letters to some fire department recruits teeling them they had been hired. City officials later said the letters should not have been sent, and the refused to hire the men. The the officials relented.

There was also the time, last year, when this bureaucratic madness landed square on Rep. Stewart McKinney (R-Conn.), the ranking Republican member of the House District Committee. He had come back to his Capitol Hill townhouse from a long rip and tried to take a hot shower. No water. His water had been shut off by the city, supposedly for non-payment of the water bill. The next morning, holding the check the city had cashed, the congressman called the District Building and was told he had not paid. It was two days before the man who exercises much influence over a billion-dollar city budget got his water turned on.

"When you start talking to people on the Hill about the District," says McKinney, "all you hear are horror stores about how something got fouled up. There's very little sympathy to be had when the city turns your water off and you've paid the bill."

Before the 1982 race for mayor of Washington starts to get hot and heavy, let it be said that the No. 1 issue of local government is still the issue that was No. 1 when the first election was held in 1974: a bungling bureaucracy.

The bureaucracy that can't get the water bills straight or the unemployment checks out on time is the same bureaucracy that was unable to tell voters for over a year how large the city deficit ws and that regularly has real estate taxes in a mess. Even to get a permit to build a fence takes days. Half of the District's businesses say they are thinking of moving out, according to a city-sponsored survey, and one of the reasons, 73 percent of them say, is that they find it impossible to deal with a city government that is incompetent. That incompetence is stealing dollars and jobs from the city.

This is the issue that Marion Barry scored the most points with in his campaign three years ago. He protrayed Walter Washington as a kindly old man not quite up to making the government snap into line, and Sterling Tucker as a younger version of Walter Washington.

"It's the people that have to be the focus of this campaign," Barry said in the heat of campaign outrage in 1978."People are embarrassed to say 'I'm from the District of Columbia.'"

After his election, Barry brought in "can-do" administrators to make the city work, and his transition team made a public display of how bad things had been under the old administration. But the results from the Barry administration in making the bureaucracy work have been minimal. The tax bills are still a mess, and the summer jobs program was a fiasco for two of three years; in the third year, the checks finally got to the teen-agers, but the quality of the program was not nearly as good as it could have been.

Early in his second year in office, Barry began saying that it was harder than he imagined to make the bureaucrats do good work. His single triumph over the bad guys was to streamline the procedure for renewing driver's licenses; it now takes 15 to 20 minutes to get a new license.

But the grand effort of efforts by Barry to wrestle the untamed bureaucracy into submission was sent his righthand man, Ivanhoe Donaldson, to run the Department of Employment Services, the agency that handles the summer jobs program and unemployment checks. Donaldson has been in charge 11 months now, and he is still trying to make the agency work; witness the problems with the new unemployment check system.

"This was just a kind of lethargic bureaucracy," Donaldson said in a May interview, seven months into his crusade. "It needs to have a little juice pumped into it. We had half the senior officials in acting positions. They didn't feel that they were in charge.The staff members who deliver services eyeball to eyeball with people, over the counter, were under tremendous stress, but they had no stress training. They didn't know where they stood in their careers, because there was no career ladder, and they didn't see the connection between doing a good job and moving up. What we had was a lot of frustration. Just to say 'Treat the public nice' was not enough."

After firing a dozen people, by his own estimates, and forcing even more to take jobs elsewhere, under threat of being fired, Donaldson thinks the employment services apparatus -- despite current problems -- is doing a better job than ever.

"We're improving. But we're not as good as we should be. If passing is 65, and you get a 20, you've failed. That's been our story. Well, now we're scoring 40. It's 100 percent improvement over the first score, but it's still a failure."

Donaldson's assessment may be right. But how is one to know? By his own admission, his bureaucracy is still failing. Until it begins to get passing grades, to do a few things passably well, it will be hard to tell what is real improvement and what is another round of promises to get the bureaucracy to work.

In the 1982 election, if there is a candidate who harps on making this city's bureaucracy work, he will probably win in a landslide. City residents, especially the unemployed, are tired of hearing that the check is in the mail.