Trey Parker and Matt Stone put an Oscar-wielding Phil Collins parody in this episode mainly because Collins had beat them at the Oscars in the category 'Best Original Song' earlier.
This episode deals with the controversy around underground recording artist Wesley Willis and his battle with Schizophrenia. Many felt it was wrong to listen to his music because it could be seen as mocking Willis.
The question that Timmy fails to answer and leads to his diagnosis of ADD is: "What kind of car did Gatsby drive?" This is not as capricious as it first appears, as Gatsby's car (a yellow Rolls Royce) is actually fairly important to the plot of "The Great Gatsby".
The reading of "The Great Gatsby" to see if Timmy has ADD is a reference to Andy Kaufman who would do the same to his audience. Though, despite popular belief, he never actually read the entire book. Usually just far enough to agrivate the audience into having them agree to put on a record instead. (But the record would usually be just a recording of Kaufman still reading "The Great Gatsby").