China

Claim: Obama said Romney invested in a company that is helping Chinese authorities spy on its people.

Facts: In December 2011, a Bain-run fund in which a Romney family blind trust has holdings purchased the video surveillance division of a Chinese company, Uniview Technologies, according to a March report in The New York Times. Uniview is the largest supplier to the government's Safe Cities program, a controversial monitoring system that allows the Chinese authorities to watch over university campuses, places of worship and other gathering places through centralized command posts.

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In his unsuccessful 1994 Senate campaign against Sen. Edward Kennedy, D-Mass., Romney at the time criticized the senator for using a blind trust to manage his investments, calling it "an age-old ruse." He added, "You can always tell the blind trust what it can and cannot do. You give a blind trust rules."

Immigration

Claim: Obama said Romney called Arizona's controversial immigration law a "model" for the rest of the nation.

Facts: Romney quickly corrected Obama on this one, saying he was referring only to the E-verify provision of the Arizona law.

"You know, I think you see a model in Arizona," Romney's said in a Feb. 22 debate in Mesa, Ariz. But he continued: "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. This E-verify system allows employers in Arizona to know who's here legally and who's not here legally."

But Romney has also said he would drop the federal lawsuits challenging the constitutionality of the Arizona law "on Day One" — a position now mooted by a Supreme Court ruling that overturned some provisions of the law and upholding others.

At an event sponsored by Spanish-language Univision last month, Romney softened his stance. "My inclination would be to have them go with the rate of inflation."