THE GOVERNMENT of the District of Columbia says it will have jobs ready for 25,000 teen-agers this summer. The figure, which comes from Mayor Marion Barry, represents the biggest promise made since Mr. Barry claimed the city would find 30,000 summer jobs for youths early in his first administration. That effort fell flat on its face, to be sure. Thousands of teen-agers were left disappointed, somewhat bitter and more than a bit confused when, for example, they were sent to the wrong work places and, once sent to the right places, had difficulty getting their paychecks. Since then, however, there has been steady improvement.

The District's summer jobs program was an inefficient and outdated operation that tried to gear up once a year when the summer was almost upon us. It has since been computerized, has its own year- round staff, begins in the city's junior and senior high schools every fall, and gathers far more information on the employment interests and abilities of teen-agers and the skills needed by employers.

Last summer, the city says it used federal and city funds to finance 20,110 jobs for teen-agers. This year, District officials say they have already identified 19,271 summer jobs in government agencies and nonprofit organizations. Teen-agers hired under the program will get jobs for seven weeks at $3.35 per hour for from 20 to 40 hours per week.

A new effort is also being made this year. City officials say that letters will be sent out to some 11,000 private employers who do business in the District, encouraging them to hire city youths. Similar letters are being sent to about 250 minority firms.

They are being encouraged to join in a program that has admirable goals: giving the city's teen- agers a taste of what future jobs might offer, a worthwhile way to spend a few weeks of their summer, and the pride that comes from having one's own job.

Fortunately, it has also become a program that works about as well as any summer job effort can.