How much of the story "actually happened" in American Hustle?

Wikipedia covers the differences to reality in the article about the movie:

Historical accuracy

American Hustle does not attempt to directly document the events of Abscam. The names are changed, and the film begins with the on-screen message, "Some of this actually happened".

Major departures from reality include:

• In the film, Irving Rosenfeld begins a life of criminality when he smashes storefront windows as a child in order to provide more work for his father's glass-installation business. In real life, Melvin Weinberg began working for his father only as an adult. He did smash windows at that point, and according to one article after Abscam was revealed, it was indeed done to shore up business for Weinberg's father.[27] A later report, however, states that it was done at the behest of the local union, to punish businesses who used non-union glaziers.[28]

• In the film, Camden mayor Carmine Polito is shown as a selfless politician who gets involved in the scam only to provide jobs to his constituents; Irving feels so bad for Carmine that he engineers a reduced sentence for him. In reality, though Camden mayor Angelo Errichetti was widely praised for caring about the people of Camden, he also had a reputation for committing crimes. During the Abscam operation, he offered to get the fake sheikh into illegal businesses such as money counterfeiting and drug smuggling. Though Weinberg developed a fondness for Errichetti as a man who "didn't beat around the bush", he made no attempt to protect Errichetti from prosecution.[28]

• Evelyn Knight, Weinberg's mistress on whom the character of Sydney Prosser is based, was involved in Weinberg's scams, though to a lesser extent than shown in the film; and she was not involved in Abscam. She was also English, not an American impersonating an English woman as shown in the film.[7]

• Weinberg's wife Cynthia Marie Weinberg, the basis for Rosalyn Rosenfeld, is not known to have had an affair with someone from the mafia, nor did she nearly blow Weinberg's cover.[29]

• The character of Richie DiMaso is based to some extent on federal agent Tony Amoroso, although in real life Amoroso was just one of a number of agents involved in setting up and executing the scam.[29]

• In the film, the sheikh is impersonated by a Mexican-American FBI agent who spoke Arabic. In real life, the sheikh was played by two different agents: first briefly by an American, Mike Denehy, who spoke no Arabic, then by a Lebanese-American.[28][29]

The "real" story is covered in the article about Abscam.