The end of the episode features a scene with Quagmire running down a field. This is the same as the ending of Little House of the Prarie, in where Laura Inglis does the same thing.
Airplane: Although the title of the episode is Airport '07 the show does not pay homage to the Airport movies directly, but makes a great many refferences to the parody movie Airplane including: The Sound of Airplane that Peter and the Gang are on, the conversation Glenn has with Hugh Heffner ends the same way the conversation in Airplane ends between the Doctor and Ted Striker, and the music used in the scenes is also lifted from Airplane.
My Pet Goat: The book Mayor West is reading is "My Pet Goat" and is interrupted the same as George W. Bush was when he was told of the attack on the World Trade Center. There is of course no refference in My Pet Goat to Grey's Anatomy.