FOUR YEARS AGO today, we joined in this city's warm welcome and its hopes for great strides under a new local administration headed by Marion Barry. As expected, Mayor Barry's confident pledges of improved performance in city hall would give way to a mixture of accomplishments and failures. What is called for in the second term?

In his inaugural speech yesterday, Mr. Barry cited "themes" that at once encompass idealism and harsh economic realities--all directly affecting the people who live here. Who can quarrel with an objective of providing everyone an opportunity to be self-sufficient, well educated, well served by local government, protected from crime and assured of swift and fair criminal justice? Better to talk about what can be done rather than what cannot--and to take charge, even if it invites charges of "bossism." If the boss cannot energize his bureaucracy or does not make good on his pledges, he--not subordinates --should be held accountable.

Before the campaign last summer, we proposed an agenda for the next mayor that shared Mr. Barry's concerns about increasing protections against crime, improving the condition and supply of housing, inspiring more economic development, improving routine city services and maintaining strong management and rigorous budgeting. And since then, we have added to the mayor's list a desperate need to guarantee accurate, democratic elections from start to finish, and the importance of having a mayor who is accessible to--and listens to--the public.

If the grand rearrangement of top subordinates for the second term is to produce results, it will not come merely because those most loyal to the mayor have survived. As Mr. Barry should know--since it was key to his first election as mayor--a mayor who puts loyalty ahead of talent and energy may wind up with a sluggish, uninspired bureaucracy that produces excuses instead of results.

However unthrilling the attention to financial management may seem to the public or Mr. Barry himself, the progress of this administration in the last four years is not enough for him to abandon close oversight in favor of the other "themes." Nothing we have seen so far offers any reason to believe that the financial challenges in store for all cities will lessen. On the contrary, they are likely to test the leadership in city hall as never before.