The derivation also implicitly assumes that the gravitational potential of the Milky Way is axisymmetric and always directed towards the center. This ignores the effects of spiral arms and the Galaxy's bar. Finally, both transverse velocity and distance are notoriously difficult to measure for objects which are not relatively nearby.
The calculation relies on the assumption that the Milky Way's gravitational potential is symmetrical and always points towards its center. However, this ignores the influence of spiral arms and the Galaxy's bar. Furthermore, measuring both transverse velocity and distance for distant objects can be challenging.