President Reagan went to a familiar well in his news conference Tuesday night and an appearance yesterday in Virginia, blaming the Democrats for the nation's economic ills. But he also was dogged by a familiar problem: he made numerous factual mistakes in his claims about the economy.

Those mistakes were being underscored by Democrats yesterday even as Reagan took to the road in Virginia with his contention that "America went backward during those four Democratic years" under President Carter, years which "marked the culmination of decades of overindulgence by the liberal Washington establishment."

In making his case at the news conference that he had pulled the nation "back from the brink of disaster" and that Americans are "better off than we were" before he took office, Reagan stumbled, as he often has at news conferences, on economic statistics.

For example, the president asserted that "for four quarters we have seen a growth in the Gross National Product." In fact, inflation-adjusted GNP has been contracting for two of the last four quarters, and expanding for two.

Reagan also made the argument that even though unemployment is now at post-Depression peaks, the jobless rate was rising just as fast at the end of the Carter administration. "And certainly the rate of increase in unemployment in the last six months of 1980 was just about as great as it's been at any time since," the president said.

In fact, unemployment declined in the last six months of 1980, from 7.8 percent in July to 7.3 percent in December. The increase in joblessness that year came during the brief but sharp recession of the first six months, a period in which Reagan was almost daily campaigning against the president on this basis.

Offering good news to counter the bad, the president conceded that unemployment in the report coming out next week, the last before the election, might hit 10 percent, but he added, "I would also like to point out that there is a higher percentage of eligible workers in the land . . . everyone over age 16, man and woman, that there is a higher percentage employed today than has been true even in the past, in times of full employment."

Reagan's point is partly correct: a larger percentage of the population is in the workforce now than in the past. This is because so many more women are seeking work. But he was not correct in suggesting that a larger percentage than ever before are working.

The Bureau of Labor Statistics' employment/population ratio, which measures the percent of population over 16 years old that is employed, is now at 57.1 percent, compared with a peak of 59.2 percent in 1979.

"We know that for the last several months there has been an increase in auto sales," the president said in making his case that the economy is turning a corner.

In fact, auto sales did turn up during a 10-day period this month. But it was the first upturn in sales since May, and analysts said it was largely due to incentives offered by the manufacturers to clear out cars from the 1982 model year.

The president also pointed to the help-wanted advertising in newspapers as evidence that jobs do exist for the workers who have skills. He recalled that he had pointed to the employment advertising last spring.

"And if you look at them, they're all for people with particular training or skills and so forth," the president said. "There are still that many help-wanted ads, meaning there are that many open jobs looking for someone to fill them."

But to the Conference Board, a New York business research organization that monitors help-wanted advertising in 51 daily metropolitan newspapers across the nation, maintains a comparative index of such advertising in which 1967 levels equal 100. The index stood at 130 in February, 1981, Reagan's first full month in office. It has been sliding almost constantly since then.

Yesterday, the Conference Board said help-wanted advertising had lost further ground in August and the index now stands at 78, compared with July's reading of 83. Kenneth Goldstein, a Conference Board economist, said this continuing weakness in demand for labor signals that unemployment could go even higher.

One administration official said yesterday that the White House was pleased with the news conference and described Reagan's errors as "de minimus."

Democrats were quick to seize on the mistakes, however, as national chairman Charles T. Manatt said Reagan got his facts "just flat wrong" and described the president as "The Great Prevaricator," although Manatt said he didn't want to call Reagan a "liar."