  We use N-body-spectro-photometric simulations to investigate the impact of
incompleteness and incorrect redshifts in spectroscopic surveys to photometric
redshift training and calibration and the resulting effects on cosmological
parameter estimation from weak lensing shear-shear correlations. The photometry
of the simulations is modeled after the upcoming Dark Energy Survey and the
spectroscopy is based on a low/intermediate resolution spectrograph with
wavelength coverage of 5500{\AA} < {\lambda} < 9500{\AA}. The principal
systematic errors that such a spectroscopic follow-up encounters are
incompleteness (inability to obtain spectroscopic redshifts for certain
galaxies) and wrong redshifts. Encouragingly, we find that a neural
network-based approach can effectively describe the spectroscopic
incompleteness in terms of the galaxies' colors, so that the spectroscopic
selection can be applied to the photometric sample. Hence, we find that
spectroscopic incompleteness yields no appreciable biases to cosmology,
although the statistical constraints degrade somewhat because the photometric
survey has to be culled to match the spectroscopic selection. Unfortunately,
wrong redshifts have a more severe impact: the cosmological biases are
intolerable if more than a percent of the spectroscopic redshifts are
incorrect. Moreover, we find that incorrect redshifts can also substantially
degrade the accuracy of training set based photo-z estimators. The main problem
is the difficulty of obtaining redshifts, either spectroscopically or
photometrically, for objects at z > 1.3. We discuss several approaches for
reducing the cosmological biases, in particular finding that photo-z error
estimators can reduce biases appreciably.
