  Nowadays pseudopotential density-functional theory calculations constitute
the standard approach to tackle solid-state electronic problems.
  These rely on distributed pseudopotential tables that were built from
all-electron atomic calculations using few popular semi-local
exchange-correlation functionals, while pseudopotentials based on more modern
functionals, like meta-GGA and hybrid functionals, or for many-body methods,
such as $GW$, are often not available.
  Because of this, employing pseudopotentials created with inconsistent
exchange-correlation functionals has become a common practice.
  Our aim is to quantify systematically the error in the determination of the
electronic band gap when cross-functional pseudopotential calculations are
performed. To this end we compare band gaps obtained with norm-conserving
pseudopotentials or the projector-augmented wave method with all-electron
calculations for a large dataset of 473 solids. We focus in particular on
density functionals that were designed specifically for band-gap calculations.
  On average, the absolute error is about 0.1 eV, yielding absolute relative
errors in the 5-10\% range. Considering that typical errors stemming from the
choice of the functional are usually larger, we conclude that the effect of
choosing an inconsistent pseudopotential is rather harmless for most
applications.
  However, we find specific cases where absolute errors can be larger than 1
eV, or others where relative errors can amount to a large fraction of the band
gap.
