Accidentally Correct Writing: The scene in episode 2 where Haruko mentions Misuzu thinking that dinosaurs came from chicken eggs. Misuzu's right, you know. Feathers, air sacs, four-chambered hearts, gizzards, gastroliths, toothed beaks in some birds, pubis bone moved backward into the bird-hipped configuration among some theropods, insulating wings—there's no two-ways about it: Birds are living dinosaurs.
Cowboy BeBop at His Computer: DVD advertisements describe Kanon as "a prequel to AIR, featuring the same characters". No, and no, despite the Continuity Cameo above; they take place in the same universe, but the AIR cast doesn't show up. Speaking of the ads, magazine print ads claim that it's from the creators of "Hurai Suzumiya," when it's actually just by the same studio, and, uh, it's "Haruhi."
Self-Reference: In the dream festival, where Misuzu gets a chick, Haruko is wearing a T-shirt with the Air logo.