THOUGH NOBODY HAS top jobs to offer every unemployed person in the city, some good opportunities do arise. Right now the local government has leads on training for a number of careers. Here, as in various other parts of the country, there is an apprenticeship program that offers instruction in a variety of skills and occupations. And contrary to what may be popular belief in neighborhoods of high unemployment, there are openings for those who meet basic qualifications and demonstrate certain aptitudes.

City officials, however, report some disappointment at responses to the program, including a less than overwhelming turnout at a recent workshop held to discuss apprenticeship opportunities and to recruit new applicants. Spreading the word in the right places may be one difficulty. Another may be that potential applicants are not sure what apprenticeships involve.

Activities here are governed by a D.C. Apprenticeship Council of people in private as well as public agencies, working with the D.C. Department of Employment Services. The system includes specified hours of on-the-job training under the supervision of veterans in all sorts of trades, from building construction to graphic arts, printing, communications and the culinary arts. Currently there are about 600 people enrolled in these programs, which vary in duration from one to five years.

Though some programs have no ceiling on age, the general range is 18 to 26. Requirements include a high school diploma or equivalent and successful passage of an aptitude exam. Extra points may be awarded for completion of certain high school courses or grades in certain subjects and for work experience. A number of centers around town have information, and their location and other help is available by calling 639-1676.