He appeared to wrongly claim that he was responsible for a vast reduction in the price of the F-35 jet, as well as falsely characterising a report into the problems of immigration.
The President's speech made contested claims about the value of immigration, his success in office, his plans for tax reform, and healthcare coverage.
While much of the speech was focused on the same rhetoric that Mr Trump led his campaign with – including a commitment to bring jobs back to the US and boost the military – he also made a number of factual claims about his work as president.
Here are some of those false claims in full, as fact checked by the Associated Press.
TRUMP: "According to the National Academy of Sciences, our current immigration system costs America's taxpayers many billions of dollars a year."
THE FACTS: That's not exactly what that report says. It says immigrants "contribute to government finances by paying taxes and add expenditures by consuming public services."
The report found that while first-generation immigrants are more expensive to governments than their native-born counterparts, primarily at the state and local level, immigrants' children "are among the strongest economic and fiscal contributors in the population."
The report found that the "long-run fiscal impact" of immigrants and their children would probably be seen as more positive "if their role in sustaining labour force growth and contributing to innovation and entrepreneurial activity were taken into account."
TRUMP: "We've saved taxpayers hundreds of millions of dollars by bringing down the price" of the F-35 jet fighter.
THE FACTS: The cost savings he persists in bragging about were secured in full or large part before he became president.
The head of the Air Force program announced significant price reductions in the contract for the Lockheed F-35 fighter jet Dec. 19 — after Trump had tweeted about the cost but weeks before he met the company's CEO about it.
Pentagon managers took action even before the election to save money on the contract. Richard Aboulafia, an analyst with the aerospace consulting firm Teal Group, said there is no evidence of any additional cost savings as a result of Trump's actions.
TRUMP: "We will provide massive tax relief for the middle class."
THE FACTS: Trump has provided little detail on how this would happen. Independent analyses of his campaign's tax proposals found that most of the benefits would flow to the wealthiest families. The richest 1 percent would see an average tax cut of nearly $215,000 a year, while the middle one-fifth of the population would get a cut of just $1,010, according to the Tax Policy Center, a joint project by the Brookings Institution and Urban Institute.
TRUMP: "Ninety-four million Americans are out of the labour force."
THE FACTS: That's true, but for the vast majority of them, it's because they choose to be.
That 94 million figure includes everyone aged 16 and older who doesn't have a job and isn't looking for one. So it includes retirees, parents who are staying home to raise children, and high school and college students who are studying rather than working.
They are unlikely to work regardless of the state of the economy. With the huge baby-boomer generation reaching retirement age and many of them retiring, the population of those out of the labor force is increasing and will continue to do so, most economists forecast.
It's true that some of those out of the workforce are of working age and have given up looking for work. But that number is probably a small fraction of the 94 million Trump cited.
TRUMP: "Obamacare is collapsing ... imploding Obamacare disaster."
THE FACTS: There are problems with the 2010 health care law, but whether it's collapsing is hotly disputed.
One of the two major components of the Affordable Care Act has seen a spike in premiums and a drop in participation from insurers. But the other component, equally important, seems to be working fairly well, even if its costs are a concern.
Trump and congressional Republicans want to repeal the whole thing, which risks leaving millions of people uninsured if the replacement plan has shortcomings. Some critics say GOP rhetoric itself is making things worse by creating uncertainty about the future.
The health law offers subsidised private health insurance along with a state option to expand Medicaid for low-income people. Together, the two arms of the program cover more than 20 million people.
Republican governors whose states have expanded Medicaid are trying to find a way to persuade Congress and the administration to keep the expansion, and maybe even build on it, while imposing limits on the long-term costs of Medicaid.
While the Medicaid expansion seems to be working, the markets for subsidised private health insurance are stressed in many states. Also affected are millions of people who buy individual policies outside the government markets, and face the same high premiums with no financial help from the health law.
Larry Levitt of the nonpartisan Kaiser Family Foundation says "implosion" is too strong a term. An AP count found that 12.2 million people signed up for this year, despite the Trump administration's threats to repeal the law.
But a health care blogger and industry consultant, Robert Laszewski, agrees with Trump, saying too few young, healthy people have signed up to guarantee the stability of the insurance markets.
TRUMP: His budget plan will offer "one of the largest increases in national defence spending in American history".
THE FACTS: Three times in recent years, Congress raised defence budgets by larger percentages than the 54 billion dollars, or 10%, increase Mr Trump proposes. The base defence budget grew by 41 billion dollars, or 14.3%, in 2002; by 37 billion dollars, or 11.3%, in 2003, and by 47 billion dollars, or 10.9%, in 2008, according to Defence Department figures.
TRUMP: "According to data provided by the Department of Justice, the vast majority of individuals convicted for terrorism-related offences since 9/11 came here from outside of our country. We have seen the attacks at home - from Boston to San Bernardino to the Pentagon and yes, even the World Trade Centre."
THE FACTS: It is unclear what Justice Department data he's citing, but the most recent government information does not back up his claim. Just over half the people Mr Trump talks about were born in the US, according to Homeland Security Department research revealed last week. That report said of 82 people the government determined were inspired by a foreign terrorist group to attempt or carry out an attack in the US, just over half were native-born.
Even the attacks Mr Trump singled out were not entirely the work of foreigners. Syed Rizwan Farook, who along with his Pakistani wife killed 14 people in the 2015 attack in San Bernardino, California, was born in Chicago.
It is true that in the immediate aftermath of September 11, the FBI's primary concern was with terrorists from overseas feared to be plotting attacks in the US, but that is no longer the case.
The FBI and the Justice Department have been preoccupied with violent extremists from inside the US who are inspired by the calls to violence and mayhem of the Islamic State group. The Justice Department has prosecuted scores of IS-related cases since 2014, and many of the defendants are US citizens.
Additional reporting by Associated Press
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