(1) That ancient culture didn't really exist until the Greeks came along. In particular that the Greeks invented mathematics. If you point out that the Egyptians and Babylonians already had a knowledge of practical mathematics, then the Greek mathematics was the first real mathematics since they developed pure mathematics.
(2) I also came across a poster that the Greeks initiated systematic military innovation, which would have been news to the Assyrians (not to mention the Chinese.)
(3) That the Semitic alphabet wasn't really an alphabet and the important thing was when vowels were added. (Vowels weren't in the Phoenician alphabet because the basis of meaning is consonant clusters.)
(4) That some event in historical times made people human beings. That people in the past didn't have the same emotions we do. (Although they did sometimes have different views about things.)
(5) Lack of historical perspective. For instance, ask people who the worst president was, and a lot will say Clinton or Bush 43. Ask them who the most important scientist was, and they'll say someone born in the last fifty years. Ask them to list the best movie of all time, or the worst, and it's something that came out in the last ten years. [The opposite is sometimes true, and you'll see lists of the best and worst that include nothing made in the last thirty years.]