  We study the effects due to mismatches in passbands, polarization angles, and
temperature and polarization calibrations in the context of the upcoming cosmic
microwave background experiment Simons Observatory (SO). Using the SO
multi-frequency likelihood, we estimate the bias and the degradation of
constraining power in cosmological and astrophysical foreground parameters
assuming different levels of knowledge of the instrumental effects. We find
that incorrect but reasonable assumptions on the values of all the systematics
examined here can have important effects in cosmological analyses, hence
requiring marginalization approaches at likelihood level. When doing so, we
find that the most relevant effect is due to bandpass shifts. When
marginalizing over them, the posteriors of parameters describing astrophysical
microwave foregrounds (such as radio point sources or dust) get degraded, while
cosmological parameters constraints are not significantly affected.
Marginalization over polarization angles with up to 0.25$^\circ$ uncertainty
causes an irrelevant bias $\lesssim 0.05 \sigma$ in all parameters.
Marginalization over calibration factors in polarization broadens the
constraints on the effective number of relativistic degrees of freedom
$N_\mathrm{eff}$ by a factor 1.2, interpreted here as a proxy parameter for non
standard model physics targeted by high-resolution CMB measurements.
