There are two main points to note in Ryle's piece: his characterization of Descartes' dualism and the nature of the error he takes it to make.

• If it seems strange to describe dualism as an "official" doctrine, remember that Ryle wrote over 50 years ago; although criticism of dualism were hardly new then and many besides Ryle criticized it at the time, it was easier to take something like Cartesian dualism for granted in the first half of the 20th century than it came be later. Ryle's description of the view as a belief in "the Ghost in the Machine" struck a chord, and that phrase has made its way outside of professional philosophy into the broader culture. Think about his reasons for using this description and also about his reasons for calling the view a "paramechanical" hypothesis (see p. 36 c. 2).
• Your second task is to understand what Ryle means by a "category mistake" both in general and as it applies to Cartesian dualism. For a general understanding, you should certainly consider Ryle's initial examples in §2 (pp. 53-54); but also think about the example towards the end of §3 ("She came home in ..." and "three things are now rising, namely ..."--p. 38, col. 1). One way into the specific application of the idea to dualism is by thinking about the connection between describing Cartesian dualism as a paramechanical hypothesis and describing it as a category mistake.

Finally, think about the value Ryle ascribes to myths in the final section. How do you suppose he'd reply if asked why, given that myths can be valuable, there was anything wrong with continuing to believe in the Ghost in the Machine?