  Imperfect photometric calibration of galaxy surveys due to either
astrophysical or instrumental effects leads to biases in measuring galaxy
clustering and in the resulting cosmological parameter measurements. More
interestingly (and disturbingly), the spatially varying calibration also
generically leads to violations of statistical isotropy of the galaxy
clustering signal. Here we develop, for the first time, a formalism to
propagate the effects of photometric calibration variations with arbitrary
spatial dependence across the sky to the observed power spectra and to the
cosmological parameter constraints. We develop an end-to-end pipeline to study
the effects of calibration, and illustrate our results using specific examples
including Galactic dust extinction and survey-dependent magnitude limits as a
function of zenith angle of the telescope. We establish requirements on the
control of calibration so that it doesn't significantly bias constraints on
dark energy and primordial non-Gaussianity. Two principal findings are: 1)
largest-angle photometric calibration variations (dipole, quadrupole and a few
more modes, though not the monopole) are the most damaging, and 2) calibration
will need to be understood at the 0.1%-1% level (i.e. rms variations mapped out
to accuracy between 0.001 and 0.01 mag), though the precise requirement
strongly depends on the faint-end slope of the luminosity function and the
redshift distribution of galaxies in the survey.
