A Prince George's County grand jury issued a report yesterday that critizies the design, crowding and operation of the new county detention center, reported on problems within the schools and the county's federally funded jobs program, and describes its own work as disorganized, ineffective and in need of reforms.

The 23-member panel began work last April 3 and was dismissed yesterday after submitting a 10-page report on its findings.

The report chrged that the design of the new county detention center in Upper Marlboro, which opened in December, 1976, "was obsolete when built, was developed without proper consultation from correctional personnel . . . and did not incorporate the latest concepts in operational efficiency, prisoner security and prisoner saftey."

The report, noting that both the old and new detention centers are over-crowded, recommended that recreational facilities and women's accomodations be improved, that pail staffing be increased and that more riot equipment be provided to center personnel.

The report also found "a major problem" of lack of effectiveness" with the grand jury system in the county. The grand jury recommended that the terms of persons appointed to grand juries overlap to help continuity of investigations and procedures and that a new court official be appointed to help juries pursue investigations. Currently, the report said, the grand jury must rely too heavily on the state attorney's office.

The grand jury also reported:

The county's federally funded Comprehensive Education and Training Act (CETA) programs are poorly administered by officials who "are often more concerned with spending federal funds as fast as possible rather than providing effective programs."

Schools should construct fences to help their security and to prevent the use of school property for "illegitimate practices."

County police hve developed evidence of prostitution at several massage parlors and health spas. However, the grand jury made no indictments and reported only that "investigation is not completed and will continue.