The District of Columbia's $35 million-a-year automatic data-processing system is inadequately planned and managed, resulting in waste, lost revenue and unnecessary headaches for the public, according to a new study by the General Accounting Office.

The GAO credits the city government with beginning to remedy its computer problems, but said some of the deficiencies have gone uncorrected for as long as 10 years. The District began using computers in 1962 and currently uses them to manage a significant part of its $1.6 billion budget.

Key problems, GAO said, are the lack of centralized long-range planning and a high turnover of experienced computer personnel, with up to 79 jobs vacant, thus hurting city operations. GAO said it conducted the study because of longstanding concern in Congress about the city wasting money.

The study focused on computer programs used to keep track of motor vehicles, human services, tax records and other purposes. GAO said it intended to study the city's SHARE computer center, which provides support for the financial management system, the city's central bookkeeping system. However, the study did not review SHARE because key personnel there were "deeply involved solving major problems" that GAO did not name.

GAO did not pinpoint the amount of money wasted or lost through computer problems, but it cited several cases of funds being misspent or lost through avoidable computer errors.

For example, the report says, the city lost at least $125,000 in 1980 because computers allowed some25,000 motorists to renew registrations despite outstanding traffic tickets.

The Department of Transportation spent $325,000 on a new computerized traffic-ticketing system that has been plagued by problems, the report said. Since 1979, the department has been unable to update drivers' "moving violation" records and therefore an undetermined number of motorists have avoided license suspensions, it said.

The Department of Human Services failed to completely test a new computer program and therefore incorrectly issued $105,073 in food stamps that were redeemed.

City Administrator Elijah B. Rogers could not be reached for comment.