  We analyze a data set comprising 370 GW band structures composed of 61716
quasiparticle (QP) energies of two-dimensional (2D) materials spanning 14
crystal structures and 52 elements. The data results from PAW plane wave based
one-shot G$_0$W$_0$@PBE calculations with full frequency integration. We
investigate the distribution of key quantities like the QP self-energy
corrections and renormalization factor $Z$ and explore their dependence on
chemical composition and magnetic state. The linear QP approximation is
identified as a significant error source and propose schemes for controlling
and drastically reducing this error at low computational cost. We analyze the
reliability of the $1/N_\text{PW}$ basis set extrapolation and find that is
well-founded with narrow distributions of $r^2$ peaked very close to 1.
Finally, we explore the validity of the scissors operator approximation
concluding that it is generally not valid for reasonable error tolerances. Our
work represents a step towards the development of automatized workflows for
high-throughput G$_0$W$_0$ band structure calculations for solids.
