When Marion Barry began his longshot campaign for mayor, it was just one theme among many, just something he would mention toward the end of his speeches.

If elected, candidate Barry promised, he would see to it that city employes serve the public respectfully and efficiently. Callers to D.C. government agencies would get a "courteous voice on the other end of the line," in a Barry administration, he said.

Wherever he mentioned the issue -- at church services, business leaders' luncheons and civic association meetings -- Barry generated applause, often much louder and longer applause than followed his promises about health and housing and a litany of other campaign issues.

If anyone thought Barry would drop the subject after election day, that expectation has yet to be fulfilled.

"It is the duty of public servants to give service to people," the new mayor told a $30-a-plate luncheon gathering of business and labor leaders the day after his inauguaration. "Those in this government who don't do it won't be there long, civil service regulations notwithstanding."

In an effort to survey the situation as Barry begins his term in office, The Washington Post assigned a team of reporters last week to observe D.C. employes as they dealt with inquiring members of the public, to ask employes and citizens about their encounters with each other, and to place phone calls to several busy government offices.

The reporters came back with mixed findings. There were cases in which D.C. residents received quick, courteous service, but there were also tales of woe. Here are some of the situations the reporters found: 'That's Not My Department'

The cashier's window on the ground floor of the Potomac Building North, 614 H St. NW, was the third and last of Robert Gordon's stops as he sought to solve a problem about his city water bill.

He was carrying two items: a bill for $48.33 and a Sept. 29 letter from the D.C. government reporting that it had billed him previously for an "erroneous charge" of $106 for water and sewer services.

After waiting in line for about a half hour at another office a block away, Gordon said he had been instructed to sign a voucher and to expect his $106 refund in six to eight weeks. But he was also told there was no way he could apply the refund to the bill, which he would have to pay at the H Street office.

Gordon, a letter carrier, spent the better part of his day off straightening the matter out, but he was goodnatured about the experience.

"They were polite," he said. "When they get around to you, most of them are polite. But it takes so long to get anything done. Everybody you talk to says that's not my department." The Quest by Telephone

For a taxpayer with a query, stalking a piece of information through the District of Columbia government telephone system -- which has been undergoing conversion to a new Centrex technology -- can cause great frustration:

To discover whether a D.C. landlord has applied for a go-ahead to convert his rental apartments into condominiums for instance, took five phone calls and 20 minutes.

The quest began with a reporter's call to the number listed under "General Information -- Housing" in the D.C. phone book under the D.C. government listings.

The number was busy the first time a call was attempted. On the second try it rang 26 times before someone answered.

Asked the condominium question, the voice at the other end responded flatly, "You have the wrong number."

When told that the number was listed for such information, the sullen female voice said, "I know. It's a mistake." She then put the reporter on hold for more than two minutes while she searched for the list of appropriate numbers, but she finally gave up and referred instead to another general information number.

A call to that number produced an operator who said it had been changed and gave the new number.

The fourth call reached an operator who was not only friendly and polite, but who was able to direct the reporter to the fifth number, which turned out to be the right one, where an employe speedily and cheerfully came up with the information. 'I Just Walked on Through'

Sterland Covington, 49, of 48th Street NE could hardly believe it. He had walked into the Department of Motor Vehicles offices at 301 C St. NW five minutes earlier and now he was walking out with his new driver's permit.

The first clerk had taken his learner's permit, asked him one question, then punched his name, address, date of birth and social security number into her computer terminal. No problems.

The next clerk punched up the same information and gave him a copy of something that resembled the permit. He then paid a cashier $12, had his picture taken at the end of the room and he now held a warm laminated card with his likeness that was slightly larger than an open book of matches.

"I thought I would have to wait in a line," he said. "I just walked on through. I wasn't surprised. I was shocked." 'This Place Is Unreal'

"This place is unreal," grumbled Fareeda Shakir, a secretary from Anacostia, as she stood in line at the cashier's window of the Department of Vital Records, 615 Pennsylvania Ave. NW, making yet another effort to obtain a birth certificate.

Shakir explained that her ex-husband had died last spring, but the Social Security Adminstration was having trouble processing payments to her children because his death certificare had the wrong birth date on it. So she went down to the Department of the Vital Records a month ago to get his birth certificate and her own.

That first time, after waiting in line for several minutes, she reached the cashier only to be told she could not pay the $2 fee in cash. She had to have a money order. So she sent to a nearby liquor store and paid $3.30 for two $1 money orders, then went back, stood in line again and asked that the certificates be mailed to her.

Hers was, after a couple of weeks, but her ex-husband's was not.

So she went to vital records again two weeks ago, paid her money again and went to lunch. She came back an hour and 20 minutes later to find that the certificate still was not ready. She waited another 40 minutes as the clerk-receptionist read off the names of two batches of processed papers. Hers was not among them.

Finally, with a colleague waiting to give her a ride back to Anacostia, she left.

Tuesday, the first day the office was open again, she went back at 9 a.m., just as it was opening, but was told that the certificate was not there. It was being mailed, the receptionist said.

"Fine," said Shakir, "when will I get it?" In about two weeks, she was told. Two weeks? It was explained that the certificates have to go to the Municipal Building before they can be mailed.

So it was that Shakir returned Thursday at 1:45 p.m. to apply once more. She paid another dollar and her son-in-law was finally able to pick up the certificate at 4 p.m.

Shakir said she never had any problems with discourtesy during her tribulations at vital records. "You don't meet anybody to complain about. The receptionist tells you the people who are processing the papers are downstairs... You ask if you can go downstairs, but no, you can't do that. It's like Big Brother downstairs."

The computers might be at the root of the problem, Shakir speculated. "You used to be able to go down to that little room in the Municipal Building and people used their feet and their fingers and it was quicker. You'd stand in line for about 20 minutes and get the certificate."

"It's true," said Jack Crandall, the registrar of vital records, when he was interviewed later. "We used to be able to get someone a birth certificate in 20 minutes, sometimes less."

But the problem, he added, has nothing to do with computers. It takes only about a minute to find the records. The problem is that between 1966 and 1976, the number of requests rose 105 percent, while the staff was cut 41 percent. "What can you do?" he asked. The Language Barrier

"Uh oh, I don't speak Spanish," said the man who answered the Department of Human Resources' main information number. "Joe, do you speak Spanish?"

A second man came on the line and asked 72-year-old Maria Zaragoza, a retired domestic who wanted to apply for welfare benefits, if she could speak any English.

"A little," Zaragoza replied.

"Well, let's try to go ahead with that and let's see what happens."

But what happened satisfied neither party, so the man suggested Zaragoza call the Kennedy Street DHR office. "You call," he said. "They have somebody hablas espanol."

No one at Kennedy Street spoke Spanish either.

"What is your address?" Zaragoza was asked. "No we don't handle that address. Who gave you this number? Call them back and tell them they gave you the wrong number." The Numbers Game

The first time a Washington Post researcher dialed 393-3333, the City Hall complaint center, the phone was answered after just two rings. The other 25 times she tried to get through, there was only a busy signal -- until 2 p.m., when a recording announced that the complaint center had closed for the day.

On Friday, The Post reseacher called four much-used D.C. government phone numbers at half-hour intervals, to see how soon, if at all, they would be answered.

727-1000, the main number for the city government and police, was answered after 30 rings at 11 a.m., and after only one ring at 4:30 p.m. At other hours, it took from four to 13 rings.

727-5240, the number for water and sewer bill problems, was answered after a single ring at 11:30 a.m., but not until it had rung 45 times at 1 p.m. The average number of rings was 11.

727-5786, the number for garbage and trash service problems, was answered after only one or two rings on every try. 'It's Just a Mad Rush'

"People get misinformed before they come here," said Bessie Waters, supervisor of the police central records office at 300 Indiana Ave. NW. "They come here with a bad attitude because they have been from pillar to post and they have called and not gotten an answer. They are not angry at us but the have to vent their feelings on someone."

February is the month when Waters sees her angriest visitors, huge lines of motorists who have to pay their outstanding parking tickets before license renewal time, March 1.

"You get a lot of hot tempered people during tag renewal time," said Waters. "They do get disorderly to the point where they have to be locked up. Some come in from the cold with little warmth in them.

"If you hold your temper people will finally relax -- I have even had people apologize to me," she added.

The five lights on Waters telephone never stopped blinking as she talked about her encounters with the public.

The five lights on Waters' telephone never ceased. She finally answered one call and put the caller on hold to go back to talking to a reporter about the public.

"It's just a mad rush. These phones will ring and ring and ring and ring. Then they (the callers) will come down and say nobody answered the phones. That's because everybody is working."