  Extracting the properties of a binary system emitting gravitational waves
relies on models describing the last stages of the compact binary coalescence.
In this article, we study potential biases inherent to current tidal waveform
approximants for spinning and precessing systems. We perform a Bayesian study
to estimate intrinsic parameters of highly spinning binary neutron star
systems. Our analysis shows that one has to include the quadrupolar deformation
of the neutron stars due to their rotation once dimensionless spins above $\chi
\sim 0.20$ are reached, otherwise the extracted intrinsic parameters are
systematically biased. We find that at design sensitivity of Advanced LIGO and
Virgo, it seems unlikely that for GW170817-like sources a clear imprint of
precession will be visible in the analysis of the signal employing current
waveform models. However, precession effects might be detectable for unequal
mass configurations with spins larger than $\chi>0.2$. We finalize our study by
investigating possible benefits of a combined gravitational wave and
electromagnetic detection. The presence of electromagnetic counterparts help in
reducing the dimensionality of the parameter space with constraints on the sky
location, source distance, and inclination. However, we note that although a
small improvement in the estimation of the tidal deformability parameter is
seen in these cases, changes in the intrinsic parameters are overall very
small.
