Trump's convention speech fact-check

Donald Trump's keynote speech at the Republican Party Convention yesterday was supposed to be the highlight of the week. What we got was an apoplectically angry man shouting at us and telling us just how bad things in America really were. The apotheosis of his speech was: "Nobody knows the system better than me, which is why I alone can fix it."

Well, say what you will about someone with zero political experience making claims like that. More importantly, though, most of Trump's analysis of the American situation is just plain wrong. He has never let a few facts get in the way of a good emotional outburst, knowing that that is where his strength, if, any, lies. But flagrant lies should really be corrected, lest an ill-educated, partisan and gullible public be persuaded of their value. Even President Obama found Trump's claims egregious enough to merit a direct rebuttal.

America remains far and away the wealthiest country in the world by total individual wealth, and also the largest by GDP by most measures, and its economy continues to hum along (US economic data all continues to increase and improve, including GDP, GDP per capita, domestic demand, consumption, investment, industrial production, retail sales, unemployment, etc).
Trump's extreme negativity about his home country centres around three main claims:

• There is unprecedented illegal immigration, particularly from Mexico and Central America. In fact, according to the Customs and Border Protection Agency, documented immigration to the United States is currently at its lowest level since 1969, and down 18% in 2015 from the previous year. The number of undocumented aliens living in the USA has also been falling continuously since 2008, and currently lies at around 10 million (down from 12 million) in a total population of about 320 million. What's more, those illegal immigrants ("killers and rapists", according to Trump) actually commit fewer crimes than native-born Americans (with an incarceration rates among the under-40s demographic of 1.6% compared to 3.3%).
• Crime is out of control, especially in the "inner cities" (read, "black population and other minorities"). In fact, US crime is at its lowest levels in a quarter of a century. Violent crime is down at the record low levels that pertained before the 1970s (in 2014, the latest year for which reliable figures are available, the violent crime, rate was 366 per 100,000 people, less than half of America's most violent year, 1991). The murder rate is at 4.5 per 100,000, similar to rates in the 1950s and 1960s. Violent crime in big cities like New York, Los Angeles and Washington has fallen even more, and is currently at about one-third of 1970s levels. According to the FBI, crime among black American youths has dropped precipitously in the last 20 years: assault by 59%, rape by 66%, and murder by 82%. The only type of crime that has seen a large rise is mass shootings, a problem largely caused by uncontrolled gun access.
• Taxation and government spending is also out of control, which is creating an economic crisis. In fact, spending on expenditures, infrastructure and investment by all levels of government in the USA fell in 2015 to its lowest level in 66 years, including a particularly sharp drop throughout the Obama years. Indeed, government spending and taxation is at a level that has led Federal Reserve chair Janet Yellen to call for increased spending to get the economy moving again, arguing that it is currently at a dangerous low. And crisis? What crisis? As mentioned above, US economic data all continues to increase and improve (including GDP, GDP per capita, domestic demand, consumption, investment, industrial production, retail sales, unemployment, etc). Granted its trade balance is not great, and public debt continues to inch up, but neither of these are likely to improve under what little we know of Trump's proposed protectionist policies.

So, where is Donald Trump getting his figures from? He does have some figures, doesn't he?