WASHINGTON — Voters didn’t always get the straight goods when President Barack Obama and Republican Mitt Romney made their case for foreign policy and national security leadership Monday night before their last super-sized audience of the campaign. A few of their detours into domestic issues were problematic too.

Romney flubbed Middle East geography. Obama got Romney’s record as Massachusetts governor wrong.

At the same time, they injected a little more accuracy into two leading misstatements of the campaign: Romney’s claim for months that Obama went around apologizing for America, and the president’s assertion, going back to his State of the Union address in January, that the U.S. military’s exit from Afghanistan will yield money to rebuild America.

A look at some of their statements and how they compare with the facts:

ROMNEY: “Mr. President, the reason I call it an apology tour is because you went to the Middle East and you flew to Egypt and to Saudi Arabia and to Turkey and Iraq. And by the way, you skipped Israel, our closest friend in the region, but you went to the other nations. And by the way, they noticed that you skipped Israel. And then in those nations, and on Arabic TV, you said that America had been dismissive and derisive. You said that on occasion America had dictated to other nations.”

OBAMA: “Nothing Gov. Romney just said is true, starting with this notion of me apologizing. This has been probably the biggest whopper that’s been told during the course of this campaign. And every fact checker and every reporter who’s looked at it, governor, has said this is not true.”

THE FACTS: Romney has indeed repeatedly and wrongly accused the president of traveling the world early in his presidency and apologizing for U.S. behavior. Obama didn’t say “sorry” in those travels. But in this debate, Romney at last explained the context of his accusation: not that Obama apologized literally, but that he had been too deferential in his visits to Europe, Latin America and the Muslim world.

Obama said while abroad that the U.S. acted “contrary to our traditions and ideals” in its treatment of terrorist suspects, that “America has too often been selective in its promotion of democracy,” that the U.S. “certainly shares blame” for international economic turmoil and has sometimes “shown arrogance and been dismissive, even divisive” toward Europe. Yet he also praised America and its ideals.

OBAMA: “What I think the American people recognize is, after a decade of war, it’s time to do some nation-building here at home. And what we can now do is free up some resources to, for example, put Americans back to work, especially our veterans, rebuilding our roads, our bridges, our schools.”

THE FACTS: If Romney’s “apology tour” was a campaign whopper, so has been Obama’s repeated claim that ending expensive wars meant the U.S. now has money to spend at home. There is no such peace dividend because the wars were financed largely by borrowing.

Yet Obama, too, watched his words a little more carefully Monday night, with his milder suggestion that “some resources” are freed up. That’s a more plausible point, if only because U.S. “resources” include the ability to continue to go deeper in debt, but for the purpose of fixing roads, bridges and the like, instead of for making war.

ROMNEY: “Syria is Iran’s only ally in the Arab world. It’s their route to the sea.”

THE FACTS: Iran has a large southern coastline with access to the Persian Gulf and the Gulf of Oman. And it has no land border with Syria.

ROMNEY: Said that when he was Massachusetts governor, high-school students who graduated in the top quarter “got a four-year, tuition-free ride at any Massachusetts public institution of higher learning.”

OBAMA: “That happened before you came into office.”

ROMNEY: “That was actually mine, actually, Mr. President. You got that fact wrong.”

THE FACTS: Romney was right. The John and Abigail Adams scholarship program began in 2004 when he was governor.

ROMNEY: “I said that we would provide guarantees, and that was what was able to allow these (auto) companies to go through bankruptcy, to come out of bankruptcy. Under no circumstance would I do anything other than to help this industry get on its feet. And the idea that has been suggested that I would liquidate the industry. Of course not. That’s the height of silliness. I have never said I would liquidate the industry.”

OBAMA: “Gov. Romney, you keep on trying to airbrush history here. You were very clear that you 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. They would have gone through a liquidation.”

THE FACTS: It’s true that Romney didn’t preach liquidation of GM and Chrysler and that he saw his approach as a way to save the auto companies. But his was an improbable course. Opposing a government bailout, Romney instead favored private loans to finance the automakers’ restructuring in bankruptcy court. His proposed government loan guarantees would only have come after the companies went through bankruptcy. At the time, however, both automakers were nearly out of cash and were bad credit risks. The banking system was in crisis and private money wasn’t available. So without hefty government aid, the assets of both companies probably would have been sold in liquidation auctions.

ROMNEY on SYRIA: “What I’m afraid of is we’ve watched over the past year or so, first the president saying, ‘Well, we’ll let the U.N. deal with it.’ And Assad — excuse me, Kofi Annan — came in and said we’re going to try to have a cease-fire. That didn’t work. Then it went to the Russians and said, ‘Let’s see if you can do something.’ We should be playing the leadership role there.”

OBAMA: “We are playing the leadership role.”

THE FACTS: Under Obama, the United States has taken a lead in trying to organize Syria’s splintered opposition, even if the U.S. isn’t interested in military intervention or providing direct arms support to the rebels. The administration has organized dozens of meetings in Turkey and the Middle East aimed at rallying Syria’s political groups and rebel formations to agree on a common vision for a democratic future after Syrian President Bashar Assad is defeated. And Secretary of State Hillary Rodham Clinton brought dozens of nations together as part of the Friends of Syria group to combine aid efforts to Syria’s opposition and help it win the support of as many as Syrians as possible. The U.S. also is involved in vetting recipients of military aid from America’s Arab allies like Saudi Arabia and Qatar.

Romney is partly right in pointing out Obama’s failure to win U.N. support for international action in Syria. But the Friends of Syria group has helped bring in hundreds of millions of dollars in humanitarian aid and other forms of assistance to Syrian civilians and the political opposition.

OBAMA: “What I would not have had done was left 10,000 troops in Iraq that would tie us down. And that certainly would not help us in the Middle East.”

THE FACTS: Obama was suggesting that he had never favored keeping U.S. troops in Iraq beyond the December 2011 withdrawal deadline that the Bush administration had negotiated with the Iraqi government. Actually, the Obama administration tried for many months to win Iraqi agreement to keeping several thousand American troops there beyond 2011 to continue training and advising the Iraqi armed forces. The talks broke down over a disagreement on legal immunity for U.S. troops.

ROMNEY: “We have an enormous trade imbalance with China, and it’s worse this year than last year and it’s worse last year than the year before.”

THE FACTS: That’s true as far as it goes but the imbalance is far from unique to the Obama years. The U.S. has run a trade deficit with China since 1985 and the gap has widened nearly every year since. According to Chinese customs data, Beijing reported a $181.3 billion trade surplus with the United States in 2010. That grew to $202.3 billion last year. The surplus for the first nine months of this year was $161.9 billion, well ahead of the level at this point in 2011.

OBAMA: “You are familiar with jobs being shipped overseas because you invested in companies that were shipping jobs overseas. And, you know, that’s your right. I mean, that’s how our free market works.”

THE FACTS: Bain Capital, the private equity company that Romney ran from 1984 to 2001, did invest in several companies that shifted American jobs and operations from the U.S. to China and other foreign nations. In one instance in 1998, Bain bought a 10 percent investment stake in Global-Tech, a Hong Kong firm that used mainland Chinese factories to make toasters and other appliances for U.S. manufacturers that were phasing out American operations and jobs. Romney held full Bain partnership stakes in that deal before the firm sold its holding later that year. Bain also invested in several firms that outsourced to Mexico in the early 2000s, but by then Romney had begun shifting away from Bain to a role running the Winter Olympic Games in Salt Lake City. And in almost all of these cases, it remains unclear how much oversight Bain had in the overseas shifts. The Romney campaign has said that Romney’s holdings were mostly passive in nature, particularly after he left the firm.

ROMNEY: “In the 2000 debates, there was no mention of terrorism.”

THE FACTS: There was passing mention of terrorism in the 2000 debates. In the Oct. 17, 2000, debate between Democrat Al Gore and Republican George W. Bush, Gore talked about his work in Congress to “deal with the problems of terrorism and these new weapons of mass destruction.” And in the vice presidential debate, Democrat Joe Lieberman defended the Clinton administration’s record of preparing the armed forces to “meet the threats of the new generation of tomorrow, of weapons of mass destruction, of ballistic missiles, terrorism, cyber warfare.” Romney’s larger point, that the U.S. did not anticipate anything on the scale of terrorist threat that existed, is supported by the light attention paid to the subject in the debates.