  In this empirical work, we aim to quantify the systematic uncertainties in
stellar mass $(M_\star)$ estimates made from spectral energy distribution (SED)
fitting through stellar population synthesis (SPS), for galaxies in the local
Universe, by using the dynamical mass $(M_\text{dyn})$ estimator as an
SED-independent check on stellar mass. We first construct a statistical model
of the high dimensional space of galaxy properties; size $(R_e)$, velocity
dispersion $(\sigma_e)$, surface brightness $(I_e)$, mass-to-light ratio
$(M_\star/L)$, rest-frame colour, S\'ersic index $(n)$ and dynamical mass
$(M_\text{dyn})$; accounting for selection effects and covariant errors. We
disentangle the correlations among galaxy properties and find that the
variation in $M_\star/M_\text{dyn}$ is driven by $\sigma_e$, S\'ersic index and
colour. We use these parameters to calibrate an SED-independent $M_\star$
estimator, $\hat{M}_\star$. We find the random scatter of the relation
$M_\star-\hat{M}_\star$ to be $0.108\text{dex}$ and $0.147\text{dex}$ for
quiescent and star-forming galaxies respectively. Finally, we inspect the
residuals as a function of SPS parameters (dust, age, metallicity, star
formation rate) and spectral indices (H$\alpha$, H$\delta$, $D_n4000)$. For
quiescent galaxies, $\sim65\%$ of the scatter can be explained by the
uncertainty in SPS parameters, with dust and age being the largest sources of
uncertainty. For star-forming galaxies, while age and metallicity are the
leading factors, SPS parameters account for only $\sim13\%$ of the scatter.
These results leave us with remaining unmodelled scatters of $0.055\text{dex}$
and $0.122\text{dex}$ for quiescent and star-forming galaxies respectively.
This can be interpreted as a conservative limit on the precision in $M_\star$
that can be achieved via simple SPS-modelling.
