The Leveson paper is quite long, and not all parts are equally important:
Skim Sections 1 and 2. You should understand the basics of the Therac-25's design and how it was used. (You may also find this figure a helpful accompaniment to Figure 1 on page 4.)
Skim Sections 3.1-3.3, which detail a few of the Therac-25 incidents.
Read Sections 3.4 and 3.5. These detail a particular incident, the software bug that led to it, and the response to the bug. Pay close attention to 3.5.3, which describes the bug.
Skip Section 3.6. (It describes an additional incident and a different bug—feel free to read if you are interested, though)
Read Section 4 closely.
http://web.mit.edu/6.033/www/assignments/rec-therac25.html
The Leveson paper is quite long, and not all parts are equally important: