  It is routinely assumed that galaxy rotation curves are equal to their
circular velocity curves (modulo some corrections) such that they are good
dynamical mass tracers. We take a visualisation-driven approach to exploring
the limits of the validity of this assumption for a sample of $33$ low-mass
galaxies ($60<v_\mathrm{max}/\mathrm{km}\,\mathrm{s}^{-1}<120$) from the
APOSTLE suite of cosmological hydrodynamical simulations. Only $3$ of these
have rotation curves nearly equal to their circular velocity curves at $z=0$,
the rest are undergoing a wide variety of dynamical perturbations. We use our
visualisations to guide an assessment of how many galaxies are likely to be
strongly perturbed by processes in several categories: mergers/interactions
(affecting $6$/$33$ galaxies), bulk radial gas inflows ($19$/$33$), vertical
gas outflows ($15$/$33$), distortions driven by a non-spherical DM halo
($17$/$33$), warps ($8$/$33$), and winds due to motion through the IGM
($5$/$33$). Most galaxies fall into more than one of these categories; only
$5$/$33$ are not in any of them. The sum of these effects leads to an
underestimation of the low-velocity slope of the baryonic Tully-Fisher relation
($\alpha\sim 3.1$ instead of $\alpha\sim 3.9$, where $M_\mathrm{bar}\propto
v^\alpha$) that is difficult to avoid, and could plausibly be the source of a
significant portion of the observed diversity in low-mass galaxy rotation curve
shapes.
