The government's index of leading indicators slipped by 0.1 percent last month, confirming the view that the economy is now sluggish, but not in the grip of a deep recession. The very slight decline in July reported by the Commerce Department yesterday followed drops in the index of 1.6 percent in May and 1 percent in June.

The Commerce Department report showed that six of the 10 indicators that make up the index of leading indicators fell in July. The biggest falls came in the money supply and in new orders for manufactured consumer goods and materials. Other indicators contributing to a fall last month were the average work week, vendor performance, building permits and stock prices.

The indicators offsetting the fall were the layoff rate, contracts and orders for plant and equipment and change in total liquid assets. The index for the change in sensitive crude materials prices, which averages movements over four months, was level in July.

In a separate report yesterday, the Bureau of Labor Statistics said that about 21.4 million persons 16 years and older were unemployed at some time during 1980. This represents 18 percent of the total labor force last year and was an increase of nearly 3 million over 1979, the biggest rise since the 1974 recession.

During that economic slump, 20.2 percent of the work force was unemployed at some time in 1974.

High interest rates have slowed the economy and are leading to growing concern in the administration. The president complained this week that the continued high cost of borrowing was "hurting us in what we are trying to do as much as they are hurting everyone else." High interest rates add to the cost of servicing government debt, and so push up federal spending and threaten to raise the budget deficit.

However, the high rates are largely the result of the Federal Reserve Board's tight money policy, which the administration has supported. Reagan officials have said that high rates are part of the cost of bringing inflation down. The president Thursday blamed them on the legacy of his predecessor.

Although some sectors of the economy have been hit hard by the persistent high rates, most economists have been surprised that the economy has not weakened more dramatically. Total output, or gross national product, fell at an annual rate of 2.4 percent in the second quarter of this year after growing very rapidly in the first three months.

Most experts predict another decline in the current quarter, although yesterday's report on the leading indicators suggests that any decline will be only slight. The administration has said that growth will increase by the end of the year as the first of the tax cuts comes through and interest rates fall.

One glimmer of hope on interest rates came yesterday as Chemical Bank of New York announced a one-point drop in its broker loan rate from 19 percent to 18 percent. Marine Midland Bank also cut its broker loan rate this week. This rate is sometimes a guide to changes in the prime lending rate, which currently is above 20 percent.