First, that there was any such thing as "ancient Greece". (I am certainly innocent of peddling this one.) Cartledge has been at the forefront of classicists' growing understanding of the cultural diversity of the poleis (city states) of the ancient Greek world, which numbered over 1000, and were dotted over a wide area from Marseille in the west to modern Turkey in the east. Though united (according to Herodotus), by religion and language, they had different customs, political systems and even calendars – and only a handful of them united against the Persian empire in the 480s BC.
Second, that the Greeks were technologically backward (I also plead innocent, but only because I made no claim either way). They may not, according to Cartledge, have had a word for wheelbarrow - but they certainly invented the amazing Antikythera Mechanism, object of much recent research and excitement from classicists and scientists alike.
Third, that the ancient Greeks resemble their Hollywood impersonators (not guilty, or not entirely - I do point out that the Spartans didn't wear leather knickers like they do in 300). Cartledge was fairly uncompromising on this one. Such movies, he said (despite his own involvement in 300) "can be dangerous as well as enjoyable and provocative. They can pander to or influence cultural contempt or hatred." He thought the Iranians were right to see 300's depiction of the Persians as "an example of cultural denigration".
Fourth (probably a bit guilty), that the Greeks invented democracy in anything like the way that we recognise it now. Radical democracy was government by, for, and crucially of, the people, unlike our modern representative democracies. Ancient Athenians would probably have regarded the British and American political systems as oligarchic.
Brilliant. There was no uniform Greek identity then.