  Radial redshift-space distortions due to peculiar velocities and other
light-cone effects shape the maps we build of the Universe. We address the open
question of their impact onto the monopole moment of the galaxy power spectrum,
$P_0(k)$. Specifically, we use an upgraded numerical implementation of the
LIGER method to generate $140$ mock galaxy density fields for a full
Euclid-like survey and we measure $P_0(k)$ in each of them utilising a standard
estimator. We compare the spectra obtained by turning on and off different
effects. Our results show that wide-angle effects due to radial peculiar
velocities generate excess power above the level expected within the
plane-parallel approximation. They are detectable with a signal-to-noise ratio
of 2.7 for $k<0.02\,h$ Mpc$^{-1}$. Weak-lensing magnification also produces
additional power on large scales which, if the current favourite model for the
luminosity function of H$\alpha$ emitters turns out to be realistic, can only
be detected with a signal-to-noise ratio of 1.3 at best. Finally, we
demonstrate that measuring $P_0(k)$ in the standard of rest of the observer
generates an additive component reflecting the kinematic dipole overdensity
caused by the peculiar velocity. This component is characterised by a damped
oscillatory pattern on large scales. We show that this `finger of the observer'
effect is detectable in some redshift bins and suggest that its measurement
could possibly open new research directions in connection with the
determination of the cosmological parameters, the properties of the galaxy
population under study, and the dipole itself.
