The U.S. economy ended 1987 on an apparently healthy note despite all the worries following the stock market plunge in October, with the number of people with jobs still rising and the civilian unemployment rate dropping to 5.8 percent, the lowest level since mid-1979, the Labor Department reported yesterday.

Civilian employment was up 2.8 million during 1987, growing 240,000 last month. Over the course of the year, the seasonally adjusted unemployment rate fell from 6.7 percent to 5.8 percent, the department said. The rate was 5.9 percent in November.

In addition, the number of unemployed workers seeking jobs last month dipped under 7 million for the first time since early 1980, a drop of nearly 1 million in the past 12 months.

"The labor market showed strength throughout most of last year, and the December figures continued that pattern of growth," said Janet L. Norwood, commissioner of labor statistics.

Payroll employment increased by 326,000 jobs last month, substantially more than most analysts had been expecting. Nearly one-third of the new jobs were in goods-producing industries, including a gain of 40,000 in manufacturing. After lagging behind other parts of the economy for several years, manufacturers added 406,000 jobs during 1987, partly in response to a large increase in demand for U.S. goods in foreign markets.

However, there were also some scattered signs in yesterday's report that growth may be slowing. The number of people at work continued to increase last month, but the length of the average workweek fell slightly. As a result, the Labor Department's index of total hours worked nudged downward. Hours worked in the portions of the economy covered by the Federal Reserve's industrial production index were little changed, suggesting that output of the nation's factories, mines and utilities increased little if at all in December. That figure will be released Friday.

And even with all of the labor market improvement in 1986, Norwood told a Joint Economic Committee hearing, "we must still be concerned about the several types of problems that persist.

"Although the number of jobless looking for work for six months or more is down by nearly a quarter of a million since last December, this group still totals some 900,000. The number working part time even though they preferred full-time work remains more than 5 million. Minority youth continue to have difficulty in finding jobs, and the number of discouraged workers {people who have given up looking for work because they think none is available to them}, although down considerably from last year, is still 900,000," Norwood said.

Many forecasters expect labor markets to show markedly less strength in 1988. Typically, they believe economic growth will slow this year, partly as a result of the impact of falling stock prices on consumer confidence and spending. However, consumers were already cutting back a bit before the spectacular October market plunge, and so far there is little clear evidence that the market drop has affected the economy significantly.

"It's a remarkable performance," said Norman Robertson, chief economist of Mellon Bank in Pittsburgh, of the December unemployment report. "I continue to be impressed by the strength and resilience of this economy, which is now going into its sixth year of expansion."

Lawrence Chimerine of the Wefa Group forecasting firm in Bala Cynwyd, Pa., declared, "It's clear the economy is still moving forward and has lost little or no momentum after the stock market crash."

Nearly half of the new jobs in December came in service-producing industries, principally those providing health and business services. There was also a 70,000 increase in the number of government jobs, mostly at the state and local levels.

But growth in some other service-producing industries, which had been expanding rapidly, has all but stopped. Retail trade jobs increased by more than 400,000 during 1987 -- about equaling the increase in all of manufacturing -- but did not rise at all in December. Similarly, employment was up more than 170,000 over the course of the year in transportation and public utilities but showed a tiny decline last month.

In the finance, insurance and real estate area, in which many banks and brokerage firms have been announcing cuts, employment rose a scant 2,000 in December but more than 200,000 in the entire year. Norwood said it may be too soon for the effects of the employment cuts in this sector to show up.

The department's report also showed that inflationary pressures from rising wages remain moderate. The department's hourly earnings index ticked downward in December, leaving it up 2.7 percent compared with the year-earlier level. The largest increases were in finance, insurance and real estate, up 4.6 percent, and in services, up 4.8 percent. With employment likely to fall in the former, such wages gains may not be repeated this year, analysts said.

Meanwhile, hourly wages rose only 0.3 percent last year in construction and only 0.7 percent in mining. The figure for manufacturing was 2.1 percent, less than the probable increase in manufacturing productivity for the year.

By a separate unemployment measure, which includes members of the armed forces in the labor force, the unemployment rate dropped from 5.8 percent in November to 5.7 percent last month.