For his part, Romney attacked what he called "devastating" defense cuts proposed by President Obama. (Read More: Facts Take a Beating in First Presidential Debate)
"We need to have as well a strong military. Our military is second to none in the world. We're blessed with terrific soldiers, and extraordinary technology and intelligence. But the idea of a trillion dollar in cuts through sequestration and budget cuts to the military would change that," Romney said.
President Obama's budget would cut the rate of growth in defense spending — not the budget itself — by about $500 billion over ten years. Sequestration refers to $500 billion in additional cuts that would take place beginning in January if Congress and the White House cannot reach a budget agreement.
Romney then repeated a frequent claim about the state of the military.
"Our Navy is smaller now than at any time since 1917," Romney said. "I want to make sure that we have the ships that are required by our Navy. Our Air Force is older and smaller than at any time since it was founded in 1947."
President Obama ridiculed the claim by noting that there are also "fewer horses and bayonets" in the military now, thanks to changing technology. But Romney's basic numbers on the Navy and Air Force were not quite right, as we first reported in September.
The U.S. Navy History and Heritage Command says the Navy does have fewer ships now than it did at the height of World War I — 286 today versus 342 in 1917. But the Navy had even fewer ships before President Obama took office, falling to a low of 278 ships in 2007 — the smallest number since the 19th century. In fact, the number of active ships grew in the first year of the Obama presidency for the first time in four years.
As for the Air Force, the number of active duty personnel is higher now than it was when the Air Force was founded in 1947. The Air Force Personnel Center reports 329,293 active duty personnel as of June 30, compared to 305,827 in 1947 according to the Air Force Association. But the number of aircraft has fallen considerably, with 5,484 aircraft in service today according to the Air Force Association compared to 25,088 in 1947.
On China, the president accurately claimed that his administration had brought more unfair trade cases — eight — than the seven cases brought during President George W. Bush's two terms. (Read More: Obama and Romney: Why All the China-Bashing?)
But the number of cases does not tell the full story.
The Administration's decision in 2009 to seek punitive tariffs on Chinese tires, criticized by Romney at the time, has also drawn criticism from non-partisan groups like the Peterson Institute for International Economics, which wrote in April, "(E)ven on very generous assumptions about the effectiveness of the tariffs, the initiative saved a maximum of 1,200 jobs. Our analysis also shows that American buyers of car and light truck tires pay a hefty price for this exercise of trade protection."
With the U.S. economy still the top issue in the election according to polls, the candidates tried wherever they could to shift the discussion there, which meant that a foreign policy debate somehow turned to the U.S. auto bailout.
Answering a question about China, Obama jabbed Romney for his 2008 New York Times op-ed article that carried the headline "Let Detroit Go Bankrupt."
"If we had taken your advice Governor Romney about our auto industry, we'd be buying cars from China instead of selling cars to China," Obama said.
"I'm a son of Detroit. I was born in Detroit. My dad was head of a car company. I like American cars. And I would do nothing to hurt the U.S. auto industry," Romney responded. "I said these companies need to go through a managed bankruptcy. And in that process, they can get government help and government guarantees, but they need to go through bankruptcy to get rid of excess cost and the debt burden that they'd built up."
But that is not quite what Romney wrote in the article. Back then, he said government help should only provide assistance after the automakers had gone through bankruptcy restructuring.
"A managed bankruptcy may be the only path to the fundamental restructuring the industry needs. It would permit the companies to shed excess labor, pension and real estate costs. The federal government should provide guarantees for post-bankruptcy financing and assure car buyers that their warranties are not at risk," Romney wrote.
Ultimately, the taxpayers financed General Motors and Chrysler during the bankruptcy process, which most experts agree was the only way the companies could survive bankruptcy without being liquidated. With the global financial system in crisis, there was no private financing available—particularly for entities that large. So while Gov. Romney was correct in arguing that he did not call for liquidating the auto companies, the course he advocated in his op-ed may well have had that effect.
In that same article, Romney advocated something he is now critical of: increased government spending for alternative energy research.
"I believe the federal government should invest substantially more in basic research — on new energy sources, fuel-economy technology, materials science and the like — that will ultimately benefit the automotive industry, along with many others," Romney wrote. "I believe Washington should raise energy research spending to $20 billion a year, from the $4 billion that is spent today."
During a debate segment on the role of America in the world, the discussion veered to the U.S. education system, and Romney touted his record as Massachusetts governor.
"While I was governor, I was proud that our fourth graders came out number one of all 50 states in English, and then also in math. And our eighth graders number one in English and also in math. First time one state had been number one in all four measures," Romney said.
"How did we do that? Well, Republicans and Democrats came together on a bipartisan basis to put in place education principles that focused on having great teachers in the classroom."
But those bipartisan principles were put in place ten years before Romney took office, when Republican Governor William Weld and Democrats in the state legislature passed the Massachusetts Education Reform Act of 1993, a sweeping, ten-year plan that changed education funding and set new standards for students and teachers.
By the time Romney took office in 2003, the state had already tied for first place in fourth grade reading and math as well as eight grade reading, and tied for second in eighth grade math. In 2005, under Romney, the state did indeed sweep all four tests, but it is not clear how much Romney had to do with it.
With the state in a fiscal crisis in 2003, Romney's first budget cut education funding, and drew sharp criticism from the non-partisan Massachusetts Budget and Policy Center, which wrote on March 5, 2003 that the budget "does not deliver on Governor Romney's campaign promise to provide (a) spending plan that preserves essential services without raising taxes." (Read More: Why 'Fiscal Cliff' May Be Bigger Threat Than You Think)
The candidates also sparred on energy, and here, the President overreached.
"We've cut our oil imports to the lowest level in two decades because we've developed oil and natural gas," Obama said.
Oil imports are down, but not that far, according to the U.S. Department of Energy, which reports they are at their lowest level since 1999 — 13 years, not 20. Regardless, it is more than a stretch for Mr. Obama to claim credit.
The Energy Department notes the decline began in 2005, long before the President took office.
Finally, in a debate about foreign policy, Romney could have used a world map — or at least a map of the Middle East.
"Syria is Iran's only ally in the Arab world, Romney said. "It's their route to the sea."
It's a circuitous route at best.
Syria has a sea coast of its own — 112 miles along the Mediterranean — and no border with Iran, which has 1,100 miles of coastline along the Persian Gulf and the Gulf of Oman.
—By CNBC's Scott Cohn