Never let facts get in the way of a good debate. On Tuesday, Barack Obama and Mitt Romney clashed repeatedly on the issues during their second presidential confrontation, and occasionally the truth seemed to get lost among all the finger jabbing.

Claim

Obama said that the day after the attack on the consulate he called it an "act of terror". Conservatives are challenging that claim.

The facts

The transcript of the president's remarks show that he was speaking about the Benghazi attack and then noted it occurred on the anniversary of al-Qaida's 9/11 assault on the US. Obama then said: "No acts of terror will ever shake the resolve of this great nation, alter that character, or eclipse the light of the values that we stand for."

The president did not explicitly single out the Benghazi attack as an act of terror. But he did appear to be referring to it in those terms, along with 9/11. He immediately went on to speak about the deaths in Benghazi again.

The next day, September 13, in a campaign appearance in Las Vegas, Obama used similar language. "And we want to send a message all around the world — anybody who would do us harm: No act of terror will dim the light of the values that we proudly shine on the rest of the world, and no act of violence will shake the resolve of the United States of America," he said.

Romney's surprise at being called out over the claim is perhaps understandable because in the days that followed, the administration stuck to the line that the assault was a response to the anti-Muslim video. The White House sent the US ambassador to the UN, Susan Rice, to say that on television talk shows the following weekend. No mention was made of a terrorist attack.

Finally, a week after the attack, Matthew Olsen, director of the National Counterterrorism Center, called the killings a terrorist attack, but even that was not picked up by most other administration officials. In the following week the defence secretary, Leon Panetta, and other officials followed.

Claim

Romney defended his opposition to any new gun controls by saying that there was already a ban in place for fully automatic weapons

The facts

That is not correct – it is possible for civilians to own such weapons if they are prepared to go through extended federal background checks including fingerprinting and pay a $200 tax. "To say that fully automatic weapons don't exist in civilian hands is inaccurate," said Josh Sugarmann, head of the gun control advocacy group the Violence Policy Center.

But neither was Barack Obama entirely open when it came to the issue of guns. Asked what had happened to his 2008 promise to keep AK-47s out of the hands of criminals, Obama signalled that he was prepared to see "if we can get an assault weapons ban reintroduced." However, there has been no sign that the Obama administration is genuinely prepared to expend political capital on driving such a renewal of the ban through a Republican-controlled House of Representatives, or to incur by doing so the wrath of the powerful gun lobby and the National Rifle Association.

Claim

Obama accused Romney of supporting a draconian Arizona immigration law that allows police officers to ask people for identification if they suspect they have entered the United States illegally.

The facts

Romney said he had only singled out a portion of the law requiring employers to "e-verify" the legal status of employees as a model. A transcript of Romney's comment, made during a Republican primary debate, seems more or less support his version. During a discussion of immigration policy, he said: "You know, I think you see a model in Arizona. They passed a law here that says – that says that people who come here and try and find work, that the employer is required to look them up on e-verify."

However, immigration remains a sore point with Romney for many, particularly among Hispanic voters, because the former Massachusetts governor has advocated a "self-deportation" approach that aims to make undocumented immigrants uncomfortable enough to leave on their own.

Claim

Romney would not have taken Detroit "bankrupt"; instead he "recommended" auto revival plan.

The facts

The Republican candidate did not back the process that saw General Motors and Chrysler get back on its feet. He opposed using government money to bail out the carmakers, instead favouring privately financed bankruptcy restructuring. At the time, the auto industry was haemorrhaging money and US banks were in no position to loan. Under Romney's plan, it is likely both companies would have gone bust.

Claim

Obama's administration has created 5 million jobs over the last 30 months

The facts

According to the US labour department, 4.5 million jobs have been created over that stated time period. But Obama neglected to mention that in the earlier months of his tenure in the White House, America lost almost as many jobs as it has since added to the economy. So he is a net job creator, but only by a sliver.