THOUGH THERE'S no telling what Mayor Washington does every minute of the day in his fifth-floor quarters at city hall, he must be awfully busy - for only this week was he finally able to squeeze in his first, honest-to-goodness press conference in some six months. Yet during his hibernations with a handful of loyal aides, the mayor somehow finds time to form some impressions of how he should be covered and reported. The other day he held forth on the subject, professing bewilderment at what he claimed has been a neglect of stories favorable to the city. He was particularly scornful of news reports attributed to "reliable sources" when these stories are not to his liking.

This, of course, comes from the grand champion of government-by-spokesperson-news-release-leak-and-mumble. What bothers the mayor, as it does most public persons we've run into, is that he isn't reading nice things about himself nearly often enough. For example, he cited his disappointment in the coverage of events in which the Carter administration restored $10 million to a city budget request that had been cut by the Ford administration. The mayor apparently expected more to be made of his having requested such a move. Frankly, we were aware of any opposition in the Carter administration to the idea, but never mind; for the sake of the city, we'll praise the mayor if Congress will be good enough to pass the appropriation.

Another example had to do with the face the millions of inauguration visitors attended events here without any reports of their having been victimized by crime. Again, he apparently wasn't apprised of news reports and editorials citing this specific and praiseworthy record. Nor, apparently, has he noticed the many occasions on which news organizations have reported the decreases in crime, noted the inaccurary of the old "crime capital" tag given the city by President Nixon and pointed to accomplishments of the metropolitan police force.

The fact is that while some things are going pretty well, it is beyond dispute that a lot of things are going badly. And it is the things tht are going badly - the Department of Human Resources, to mention one - that are of the most urgent and compelling interest, in our view, to residents. For all we know, Mayor Washington may have a resonable explanation for why these things are going badly, and perhaps even some thoughts about how to set them right. We would like to believe this is so. But this is not an easy thing to believe of a mayor who complains - chronically - about the maltreatment he receives at the hands of the press while refusing to avail himself, more than twice a year, of a golden opportunity to do something positive about it. What better way could he ask for to improve his press relations and, at the same time, give his own account of his performance on the job than regular on-the-record meetings with local reporters?