A good resource in the first half of the narration--Mossadegh's rise to power, nationalization of oil resources, and overthrow--is All the Shah's Men by Stephen Kinzer. Just be aware that the author is writing partly to make a political point about regime change.

The film is very accurate, although, as you said, a bit simplified in its description. The early 20th century rulers of Iran signed a treaty with Britain allowing the Anglo-Iranian Oil Corporation (later BP) essentially unfettered access to the country's oil resources. Muhammed Mossadegh successful rose to power as a nationalist and populist prime minister. In 1951, he nationalized Anglo-Iranian.

This led to severe diplomatic tensions between Iran and the UK, in which the UK considered using military force, but ultimately decided to overthrow Mossadegh through a coup. Iran then cut diplomatic relations with the UK, expelling most of their spies in the process. The UK was able to convince US President Dwight Eisenhower through his Secretary of State John Foster Dulles and the CIA director, his brother Allen Dulles, to carry out the coup on behalf of the UK. The Americans were concerned that Mossadegh's nationalization of industries was a step on a road to communism, and they were concerned they might lose Iran's oil resources to the Soviet sphere of influence as a result.

Kermit Roosevelt Jr, a CIA officer in Iran, executed Operation Ajax in 1953, which overthrew Mossadegh's government and reinstalled Mohammed Reza Pahlavi as king ("shah") of Iran under the guise of a popular uprising.

This is, of course, still a simplification, but hopefully provides a little more detail. Maybe somebody else can provide some input on the 1979 revolution?

Edit: Corrected as per willpredun.

I wouldn't say any of that was wrong. The biggest oversimplification is that the revolution itself involved a number of different actors - the revolution involved liberal and Communist as well as Islamic groups. Many of those who initially helped to overthrow the Shah were happy with western liberal values such as gender equality.

The opening is mostly accurate, but I just want to point out that the overall movie story of Argo was made to be a bit more dramatic then it actually was. Yes, the Americans were altered to look like a crew, and yes they walked right through customs, but the plan was so well executed that NO ONE even had a clue what was happening. It wasn't a rouge operation conducted by one man, but a well designed task force lead by one man. It was relatively smooth operation, on account at how disorganized the Iranian airport operated at the time.

I'm paraphrasing, but my favorite quote from the book says "The best agent is the one who buys something at a store, and if the clerk had to identify the man, he would have completely forgot what he looked like." Obviously, they wanted a white, attractive guy for the movie, but in reality he was a plain man with no notable features.