The D.C. City Council this week approved Coopers and Lybrand, one of the "Big Eight" public accounting firms, as the city's independent auditor for the next four fiscal years, on a contract worth about $1.8 million.

But before approving Mayor Marion Barry's selection, the council made it clear that it must have more details in audits under this contract than it has received in the past. It was an attempt to keep better track of where budgeted money is actually spent by the executive branch.

In the past, the audit has grouped budgets and expenditures into general classifications that do not always correspond with the way the City Council has budgeted. In the future, for example, amounts expended compared with what was budgeted are to be broken down by agency.

Arthur Andersen has been the independent auditor for the past three fiscal years and will be for fiscal 1983. By law, the auditor must be changed every four years, and Coopers and Lybrand's first audit, for fiscal 1984, is to come out in early fiscal 1985.

Coopers and Lybrand has agreed that 35 percent of the contract price will be allocated to a minority firm that is an independent certified public accountant. The firm also agreed to establish an intern program for students at the University of the District of Columbia.

Legislation has been introduced to give nonunion employes at UDC and nonunion educational service employes pay increases of 6 percent to match raises given most other District government employes.

Administrative salaries at UDC would go as high as $79,395 a year, more than $5,000 above what the mayor gets. At the faculty level, the salaries would start at $17,285 for an instructor and would rise to $45,715 for a distinguished professor.

The bill was introduced by council Chairman David A. Clarke at the request of UDC's Board of Trustees.

The City Council this week gave its final approval to pay raises for about one-fourth of District government employes and raised the cap on top officials' annual pay to $63,700, meaning raises of $7,399 a year for about 140 officials as of Oct. 2.

When the committee of the whole considered the measure last week, it narrowly defeated an amendment to keep the cap on salaries at the current $56,301, but the attempt was not renewed at this week's session, and the raises were approved by voice vote.

It also gave final approval without dissent to a bill to add soft body armor to the list of standard equipment for District police officers.

Legislation was tentatively approved to require insurance companies to reduce car insurance premiums for senior citizens who complete driver safety training courses. About 20 percent of the drivers in the District are senior citizens.

Sometimes marriages are simply full of conflicts. In the case of council member Frank Smith (D-Ward 1), however, he wasn't sure this week if he had one. The City Council was considering a bill to prohibit discrimination against certain types of nonphysician health-care practitioners at hospitals, including psychologists--legislation that has been hotly debated within the health-care community for the past several months.

Noting that his wife is a practicing psychiatrist, Smith said he sought advice on whether he had a conflict because of the connection. To be on the safe side, he abstained from voting.