President Reagan, in the heat of Sunday's debate, declared that abortion is not a religious problem but "a problem of the Constitution" because an unborn child "is already protected by the Constitution, which guarantees life, liberty and the pursuit of happiness to all of us."

It is the Declaration of Independence that refers to the "unalienable" rights of "life, liberty and the pursuit of happiness," and Reagan's confusion about the nation's founding documents was just one example of slip-ups, omissions and myths exchanged by the president and Walter F. Mondale in their 100-minute encounter in Louisville.

Reagan, known for his effective use of anecdotes and one-liners, uncharacteristically seemed to outdo Mondale in citing statistics, and he appeared to have trouble with many of them. Mondale, by contrast, stressed broad statements of principle, in some instances overstating the case.

But both men were trying to cast reality as they would like the voters to see it, and each skipped lightly over the full story.

Some omissions were deliberate, such as the way Mondale skirted mention of his proposed tax increases when first asked how he would reduce the federal budget deficit. Another was Reagan's boast about the 6 million people who have gotten jobs during the recovery while failing to mention millions who lost jobs in the 1981-82 recession.

In other cases, there was such selective recollection as Reagan's claim that "the only 25 percent cut that I know of" in Social Security came during the Carter administration.

In fact, Reagan proposed cuts that would have reduced Social Security benefits by nearly 25 percent from the level that future retirees would have received. And the benefit cut he blamed on Carter was a bipartisan proposal to correct a flaw in the formula adopted in 1972, during the Nixon administration, for calculating initial monthly payments and cost-of-living increases in Social Security. The effect of the formula was to overcompensate new retirees for inflation, and it was corrected for everyone born after 1916.

Mondale accused the president of proposing $20 billion in Medicare cuts. Reagan responded, "No, I never proposed that any $20 billion should come out of Medicare."

But Reagan's fiscal 1985 budget, sent to Congress earlier this year, shows a savings of $18.7 billion over the next four years in Medicare. Most of it, however, would be cuts in payments to hospitals and doctors, although beneficiaries would have to pay somewhat more.

From the start of the debate, Reagan employed selective recollection on the deficit. Asked why he failed to keep his 1980 campaign promise to balance the budget by 1983, Reagan claimed that, "before even the Election Day" in 1980, the economy "so worsened" that "I was openly saying" a balanced budget "was no longer possible."

The president did not mention that his first economic plan, submitted to Congress a few months after he took office, proposed a balanced budget by 1984, a mark on which he never came close. Later, in a speech midway through his term, Reagan's promise had become a "personal dream."

Reagan used a litany of familiar defenses on government spending but often left out pieces of the puzzle that did not reflect favorably on his record.

For example, he said, "Whether you borrow the money or whether you simply tax it away from the people, you're taking the same amount of money out of the private sector, unless and until you bring down government's share of what it is taking" out of the economy.

He did not mention his 1980 promise to squeeze the government's share of the Gross National Product to about 19 percent and that it is now at a post-World War II high of about 24 percent.

Reagan said, "I do not, very frankly, take seriously the Congressional Budget Office projections" on the deficit because "they have been wrong on virtually all of them, including the fact that our recovery wasn't going to take place to begin with."

He did not mention that his Office of Management and Budget was also wrong on virtually every deficit projection in the same period and that CBO deficit projections have been closer to the mark than those of the OMB. Neither the CBO nor the OMB or most economists accurately predicted the 1981-82 recession. The White House issued early in Reagan's first year a set of economic projections so optimistic that they came to be known as the "rosy scenario."

Reagan also contended, correctly, that economic growth has helped bring the deficit down by $21 billion since last year and said growth in the economy "increases the revenues the government gets" and, combined with spending restraint, would produce a balanced budget "without raising taxes."

He did not mention that increases in payments on the national debt are rising because of higher interest rates. By congressional estimates, higher debt costs could cancel out benefits of faster growth during this fiscal year.

In defending his economic policies against Mondale's charge that they favored the wealthy at the expense of the poor, Reagan said:

"Now I don't think that to try and say that we were taxing the rich, and not the other way around, it just doesn't work out that way. The system is still where it was with regard to . . . the progressivity, as I've said, and that has not been changed."

But the nonpartisan Urban Institute concluded this year in its report entitled The Reagan Record that the tax cuts and increases of the president's term had shifted the burden of paying for government "slightly from higher-income taxpayers to lower-income taxpayers.

"The bottom 40 percent of families are paying proportionally more of their income in taxes, with most of the increased burden falling on the poorest 20 percent of the families, whereas the top 60 percent are paying proportionally less of their income in taxes," it said.

Mondale used fewer statistics than Reagan, but also demonstrated the techniques of overstatement.

He derided the Republican platform for saying that "from here on out, we're going to have a religious test for judges before they're selected for the federal court." He repeated this charge several times in apparent reference to the platform language on abortion. He raised the specter of judges being picked by the Rev. Jerry Falwell, leader of the Moral Majority, and asked, "Does every woman in America have to present herself before some judge picked by Jerry Falwell to clear her personal judgment?"

But the platform says only, " . . . we reaffirm our support for the appointment of judges at all levels of the judiciary who respect traditional family values and the sanctity of innocent human life."

Mondale, when questioned directly about his tax-increase proposals, responded that they treat people with annual income under $70,000 "in a way that is more beneficial than the way the president proposes with a sales tax or a flat tax."

However, Reagan has made no such proposals; instead, he has announced that the Treasury Department is studying tax options and will report its findings after the election. Recently, Treasury Secretary Donald T. Regan suggested that if reelected, Reagan would probably support a modified flat tax with a few deductions; he has indicated that his administration is not leaning toward a sales or value-added tax.

In an apparent slip, Mondale declared in the debate: "As soon as we get the economy on sound ground . . . I'd like to see the total repeal of indexing," which keeps taxpayers from being pushed into higher brackets by inflation.

Only last month, Mondale issued a detailed budget and tax plan stating that he "is committed to the principle of indexing," but that it would have to be "deferred" until the deficit could be brought down.