  The forecasted accuracy of upcoming surveys of large-scale structure cannot
be achieved without a proper quantification of the error induced by foreground
removal (or other systematics like 0-point photometry offset). Because these
errors are highly correlated on the sky, their influence is expected to be
especially important at very large scales. In this work we quantify how the
uncertainty in the visibility mask of a survey influences the measured power
spectrum of a sample of tracers of the density field and its covariance matrix.
We start from a very large set of 10,000 catalogs of dark matter halos in
periodic cosmological boxes, produced with the PINOCCHIO approximate method. To
make an analytic approach feasible, we assume luminosity-independent halo bias
and an idealized geometry for the visibility mask. We find that the power
spectrum of these biased tracers can be expressed as the sum of a cosmological
term, a mask term and a term involving their convolution. The mask and
convolution terms scale like $P\propto l^2\sigma_A^2$, where $\sigma_A^2$ is
the variance of the uncertainty on the visibility mask. With $l=30-100$ Mpc$/h$
and $\sigma_A=5-20$\%, the mask term can be significant at $k\sim0.01-0.1\
h/$Mpc, and the convolution term can amount to $\sim 1-10$\% of the total. For
the power spectrum covariance, the coupling of the convolution term with the
other two gives rise to several mixed terms, that we quantify by difference
using the mock catalogs. These are found to be of the same order of the mask
covariance, and to introduce non-diagonal terms at large scales. Then, the
power spectrum covariance matrix cannot be expressed as the sum of a
cosmological and of a mask term. Our results lie down the theoretical bases to
quantify the impact that uncertainties in the mask calibration have on the
derivation of cosmological constraints from large spectroscopic surveys.
[Abridged]
