Romney: “Health-care costs have gone up by $2,500 a family.”

Factcheck.org, the Annenberg Public Policy Center’s accuracy policy, say this is false. They cite a Kaiser Family Foundation survey (PDF) that found that between 2010 and 2011, the average health-insurance premium cost for families increased by $1,300, not $2,500, and point out that even between 2009 and 2011 the increase in average cost was only $1,700.

Obama: “I put forward a specific $4 trillion deficit-reduction plan. It’s on a website. You can look at all the numbers. What cuts we make and what revenue we raise.”

Washington Post fact-checker Glenn Kessler argues that this statement isn’t exactly true. First of all, $1 trillion of the $4 trillion the president says his budget plan will cut from the deficit was already reached a year ago, so that’s $1 trillion that’s already cut regardless of who wins the election. Kessler also points out that Obama’s $4 trillion figure includes $848 billion saved by ending the wars in Iraq and Afghanistan—money that, since ending the wars have been in the works for a while, the administration had never intended to spend in the first place. “Imagine someone borrowing $50,000 a year for college—and then declaring that they have an extra $500,000 to spend over the next decade once they graduate,” is how Kessler explains it.

Romney: “I’m not going to cut education funding. I don’t have a plan to cut education funding.”

Trip Gabriel at The New York Times notes that, contrary to this statement, Mitt Romney has suggested in the past that he would, in fact, cut the education budget. Back in the spring, reporters heard Romney tell a group of Florida donors that, as president, he would merge another federal agency with the Education Department, “or perhaps make it a heck of a lot smaller.” While the Romney-approved House budget does not specify how cuts would affect particular federal programs, the White House’s own study (PDF) on the budget finds that it drops 200,000 children from Head Start as well as other early education programs, and gets rid of 38,000 teachers and aides at underprivileged schools as well as 27,000 special-education teachers.

Obama: “Governor Romney’s central economic plan calls for a $5 trillion tax cut on top of the extension of the Bush tax cuts, so that is another trillion dollars. And $2 trillion in additional military spending that the military hasn’t asked for. That is $8 trillion.”

ABC News’s Amy Bingham and Jon Karl point to Mitt Romney’s own campaign website (PDF) to counter the president’s argument here, calling it “mostly fiction.” Despite Romney’s repeated insistence that his tax plan would be “revenue-neutral,” the only real reason Obama’s claim that his opponent would add $5 trillion to the debt isn’t exactly true is because Mitt has never specified how his tax plan would be paid for. So, as Bingham explains, “Romney’s tax plan could add $5 trillion to the deficit. But that is an estimate on an incomplete tax plan ... The issue is that no one knows what those provisions are just yet.”

Romney: President Obama brought up a nonpartisan Tax Policy Center Study (which has been declared mostly true) that says Mitt Romney’s “revenue-neutral” plan to cut taxes for all Americans by 20 percent is impossible without raising taxes on the middle class.

In response to this, Romney claimed five other studies prove the legitimacy of his plan.

The Washington Post, Salon, and Politifact all say this claim is false because these so-called studies are not exactly studies. “One was a Wall Street Journal article from Martin Feldstein, a Harvard economist and an adviser to the Romney campaign; one was from Harvey Rosen, an economist at the Griswold Center for Economic Policy Studies at Princeton University; one was by Matt Jensen, an economist with the American Enterprise Institute, a conservative think tank; and two were Wall Street Journal editorials,” Politifact explains.

Obama: Romney will turn Medicare into a “voucher program.”

Factcheck.org disputes this. “The fact is, [Romney’s plan] is structured the same as the system Obama’s health-care law sets up for subsidizing private insurance for persons under the age 65,” the site argues.

Romney: “On Medicare for current retirees, [Obama’s] cutting $716 billion from the program.”

PolitiFact says this claim—a major talking point in the Denver debate—is half true. While $716 is not a made-up number, it refers to how much the Affordable Care Act, better known as Obamacare, would take away from Medicare spending—mostly to hospitals and insurers—over 10  years. Obamacare does not, as Romney insinuated, take $716 billion away from current Medicare recipients.