NO ASSESSMENT OF a city administration's effectiveness is complete without an examination of routine government services. For any mayor of Washington, this entails more than the usual municipal checklist, because the District's "city hall" also is responsible for nearly every function of a state government. Any failure -- be it the inaudible mumblings of a rude bureaucrat on the phone or the old runaround in response to a complaint -- lingers long in the memory of a resident or businessman; improvements, understandably, tend to come more quietly. But come they do, and always with room for still more.

On balance, the city government's performance in the last four years compares favorably with that of other large cities and small states. Gone are the cobwebs of colonialism that used to be everywhere in the District Building -- from a corps of old-retainer department heads rewarded for loyalty and seniority over efficiency and intelligence, to a series of inexcusable failures even to comply with court orders demanding services required by law. Today, under city administrator Elijah B. Rogers, there is evidence that a city's government can be reduced in size and yet perform better.

The design and distribution of "supercans" has resulted in cleaner streets and alleys at a reported saving of $9 million a year. A driver's license can be picked up in minutes or a long lunch hour. The rate of street and bridge improvements has gone up from 14 miles a year to 30, and the number of repaired potholes has increased fivefold.

Mayor Barry also points to these items: tax bills, checks and refunds processed in timely fashion; a reduction from six months to an average of five weeks in the waiting period for completion of plan reviews for big construction projects; an increase of 50 percent, to 3,000, in the number of daily meals served to senior citizens; proposals to allow vehicles failing inspection to be re-inspected at local service stations or car dealers; a 90 percent reduction in false fire alarms from 1978 to 1981; a pedestrian safety program that has resulted in the city's best record in 50 years; and the recruiting of more than 110,000 hours of volunteer assistance in 1981 to compensate for recreation staff reductions.

Mr. Barry's challengers, for their part, point to failures in the record of services delivered: as Mrs. Harris notes, there are families that were without heat or hot water last winter; and there are still delays in permits and other paperwork required for business to operate in the city. More arguably, both Mrs. Jarvis and Mrs. Harris have cited high rates of infant mortality and tuberculosis in this city as responsibilities, if not exactly faults, of the Barry administration. Mr. Ray has called for still more employee productivity, courtesy and cooperation, along with more personnel training and neighborhood city halls.

These objectives surely must be kept high on the agenda. Spirit, experience, courtesy and a sense of mission are all important and subject always to improvement. The existing momentum should be all the more incentive to pursue the excellence of government service that all four candidates extol.