Fact-checking has become such an integral part of the 2012 presidential race that President Obama, in his final debate against GOP challenger Mitt Romney, actually gave a shout-out to the growing crop of truth-seekers. After Romney trotted out his well-worn line about Obama's 2009 "apology tour," Obama shot back that "every fact-checker and every reporter who's looked at it, governor, has said this is not true." But Obama had his own moments of truth-stretching in the debate. Here's a scorecard of some of the biggest points of contention in the final act of the 2012 debates:

Obama: Romney was "very clear that [he] would not provide government assistance to the U.S. auto companies, even if they went through bankruptcy. You said that they could get it in the private marketplace. That wasn't true."

The verdict: Partly true

Obama overreached here, say NPR's Mark Memmott, Scott Montgomery, and Mark Stencel. In a famous November 2008 New York Times op-ed, Romney said if the government bailed out GM and Chrysler, "you can kiss the American automotive industry goodbye," but he did propose a "managed bankruptcy" in which the federal government provides "guarantees for post-bankruptcy financing." The problem is, according to auto executives and outside experts, there would have been no post-bankrupt GM or Chrysler to help, says Jeremy W. Peters at The New York Times. In late 2008, credit markets were frozen and no private firms — not even Romney's own Bain Capital — were "looking to invest to the tune of the $80 billion the car companies needed at the time." That means "the only path through bankruptcy would have been Chapter 7 liquidation, not the more orderly Chapter 11 reorganization that the company ultimately followed" under Obama. "In the tangled debate over whether the auto industry would have survived under Romney's bankruptcy plan, Obama has the edge on the argument," says Glenn Kessler at The Washington Post.

Romney: Upon taking office, Obama "said by now we'd be at 5.4 percent unemployment."

The verdict: Mostly false

This claim stems from an economic projection two Obama economists laid out before he took office, to predict the effects of a $775 billion economic stimulus bill. The economists, Christina Romer and Jared Bernstein, added "numerous caveats and warnings" to their analysis, says Kessler, "because, after all, it was merely a projection," based on an unwritten bill. But yes, a chart on Page 4 of the report did foresee unemployment dropping to 5.4 percent by mid-2012. "The chart is now infamous, but it was never pitched as a promise," says PolitiFact. And the caveats were there for good reason: "The economy was, in fact, much worse than economists knew."

Obama: Romney "said that we should still have troops in Iraq to this day."

The verdict: Half true

Romney didn't really contest Obama's narrow point, that he thinks we should still have combat troops in Iraq, says Kessler. But ultimately, "Romney has the better part of this argument," because as he points out, Obama tried to keep troops there, too. The Obama administration attempted to negotiate a Status of Forces Agreement that would keep roughly 5,000 troops in Iraq, but the talks fell apart when Iraq declined to put the agreement to a parliamentary vote and the Obama administration decided that would expose U.S. troops to Iraqi prosecution. The upshot is that Obama now "stresses the fact that he has removed all troops from Iraq, while knocking Romney for supporting what he originally had hoped to achieve."

Romney: "Our Navy is smaller now than at any time since 1917.... Our Air Force is older and smaller than at any time since it was founded in 1947."

The verdict: Pants on fire

"Judging by the numbers alone, Romney was close to accurate," says PolitiFact: In 1916, the Navy had 245 active ships, higher than the numbers before Obama took office but lower than the 285 active ships in 2009 onward; with the Air Force, the total 2009 fleet of 5,988 aircraft is smaller than in any year since 1950. But "this is a great example of a politician using more or less accurate statistics to make a meaningless claim." The ships and aircraft we have now are hugely more powerful, and unlike 50 years ago, U.S. military power is now unequaled. As University of Georgia historian William W. Stueck tells PolitiFact, Romney's comparison "doesn't pass 'the giggle test.'"

Obama: Romney called Russia "the biggest geopolitical threat facing America."

The verdict: True

In a March 26 interview on CNN, Romney said that Russia "is without question our No. 1 geopolitical foe." In both that interview and a July follow-up on CNN in which he doubled down on Russia being "the No. 1 adversary" in terms of geopolitics — "I'm talking about votes at the United Nations and actions of a geopolitical nature" — Romney added that the biggest national security threat is a nuclear Iran, not Russia.

Romney: Obama began his term with "an apology tour, of going to various nations in the Middle East and criticizing America."

The verdict: Pants on fire

In the debate, Obama called the "apology tour" line "probably the biggest whopper that's been told during the course of this campaign," and the fact-checkers agree. The idea that Obama traveled abroad and apologized for America "is a persistent and false Republican talking point that we have debunked a number of times," says PolitiFact. It stems from a Wall Street Journal op-ed by Karl Rove, says David Sessions at The Daily Beast, and "almost instantly, the right-wing blogosphere began savaging the president's attempt at diplomacy, taking up Rove's 'apology tour' moniker" to try and paint Obama as "weak and confused, reminiscent of Jimmy Carter." That it's patently false should be obvious, but "the president's actual record is what makes the 'apology tour' rhetoric most absurd." You can say a lot about Obama's legally questionable tactics to decimate al Qaeda's leadership ranks, for example, "but you can't say they were the work of an apologizer."

Obama: "Veterans' unemployment is actually now lower than [in the] general population. It was higher when I came into office."

The verdict: Half true

"Whichever measure you use, Obama's formulation was half-right" — and half-wrong, says PolitiFact. If you count all veterans, unemployment was lower (7.4 percent) than the general population (7.8 percent) when Obama took office, and is even lower (6.7 percent) now. If you look just at veterans who served post-9/11, the jobless rate was higher (8.9 percent) when Obama took office and is higher (9.7 percent) still today.

Romney: In terms of balancing budgets, "I went to the Olympics that was out of balance, and we got it on balance."

The verdict: Mostly true

"It's important to understand that there is not one budget for the Olympic Games — there are two," says PolitiFact. In terms of the private organization, the Salt Lake Organizing Committee, which ran the games, Romney did turn the finances around, not just balancing the budget but also leaving a $100 million surplus. But there's also the second budget, comprising federal dollars mostly for security and transportation upgrades. Estimates for how much the government chipped in range from $400 million to $1.5 billion, and Romney, by his own account, was aggressive in seeking federal funds for the games. "Romney is right on a technicality that misses the major issue about financing any Olympics," Stanford economist Roger G. Noll tells PolitiFact.

Obama: "With respect to what we've done with China already, U.S. exports have doubled since I came into office."

The verdict: False

According to the U.S. China Business Council, U.S. exports to China hit a record $103.9 billion in 2011, from $69.5 billion in 2009. Ten states have doubled their exports to China in that period, but the U.S. as a whole has not.

Romney: Syria is Iran's "route to the sea."

The verdict: False

This one might fit better in the gaffe column, say NPR's Memmott, Montgomery, and Stencel. Iran, "of course, has an extensive coastline along both the Persian Gulf and the Arabian Sea."

Final score: There was a lot of cherry-picking numbers and stomping on nuance by both candidates, but by choosing to repeat the "pants on fire," "four Pinocchios" claim about Obama's "apology tour," Romney wins the dubious distinction of telling the night's biggest whopper.

Sources: The Daily Beast, National Journal, The New York Times, NPR, PolitiFact, The Washington Post (2)