The study of free fall is thoroughly present in physics teaching at all levels. From the point of view of Newtonian dynamics it appears to be extremely simple, as it consists of a two-body problem with a constant force generating a constant acceleration. However, there are several important conceptual subtleties and hidden assumptions involved in this problem, which are rarely discussed in educational settings. In this work we present some of these subtleties and argue that explicitly addressing them has significant pedagogical benefits.