THE PRESIDENCY of the University of the District of Columbia is as difficult a job as any in American higher education. The university is young as institutions go; it lacks the steadying base of long experience; and there has always been an unsettling tension over its purpose. It is an open-enrollment school that aspires to have high standards. It seeks to be both accessible and convincing, and in obvious ways, as they always will anywhere, these two worthy goals have collided.

When Robert L. Green was brought here as the third president of the university in 1983, he had no prior experience running an organization of its size (about 13,000 students and 1,300 employees, a budget of about $70 million a year). He was nevertheless the unanimous choice of the 15 trustees, 11 of whom are named by the mayor. His predecessor had been abrasive and, partly because of that, unsuccessful. Dr. Green seemed well suited to deal with the university's many constituencies, and was a figure of hope.

Instead, his administration is now caught up in a complex dispute over his care and probity in the expenditure of university funds. The charges against him are laid out on the back page of this section today, together with his responses, excerpts from a report he made to the trustees late last month and views of the chairman and an alumni member of the board. In our view, some of the charges against him have been overstated. In some of the cases where he has been accused of having "misspent" funds, the problem is not that the money went for impermissible things, but that it came from the wrong accounts. These are bookkeeping arguments.

Some of the items complained of are also petty -- or would be, standing alone. Many would have gone unremarked or been one-day wonders, easily brushed aside. But Dr. Green's problem is partly that they do not stand alone. No one wants the president of UDC to lead a life of penury and self- denial. But there are plainly limits in the opposite direction as well, and on several occasions Dr. Green has appeared indifferent to these. Liberal payments have also been made in the form of consultants' fees to several previous associates of his. These are the most troubling part of the record. In some cases the work the recipients did neither merited what they were paid nor fully explains it.

When Dr. Green came here it seemed he might lift a burden from the university. Now the opposite is true: he carries a burden of his own. The board plainly has a decision to make; its chairman says it understands that. He asks for the time and maneuvering room to act in a fair and prudent way, and of course the board should have and take that. But whatever it decides as to Dr. Green, it must make certain that the practices that have led to the present embarrassment do not recur. UDC is too important an institution in this city, and still too easily hurt, to let this happen to it again.