  Current and future weak lensing surveys will rely on photometrically
estimated redshifts of very large numbers of galaxies. In this paper, we
address several different aspects of the demanding photo-z performance that
will be required for future experiments, such as the proposed ESA Euclid
mission. It is first shown that the proposed all-sky near-infrared photometry
from Euclid, in combination with anticipated ground-based photometry (e.g.
PanStarrs-2 or DES) should yield the required precision in individual photo-z
of sigma(z) < 0.05(1+z) at I_AB < 24.5. Simple a priori rejection schemes based
on the photometry alone can be tuned to recognise objects with wildly
discrepant photo-z and to reduce the outlier fraction to < 0.25% with only
modest loss of otherwise usable objects. Turning to the more challenging
problem of determining the mean redshift <z> of a set of galaxies to a
precision of 0.002(1+z) we argue that, for many different reasons, this is best
accomplished by relying on the photo-z themselves rather than on the direct
measurement of <z> from spectroscopic redshifts of a representative subset of
the galaxies. A simple adaptive scheme based on the statistical properties of
the photo-z likelihood functions is shown to meet this stringent systematic
requirement. We also examine the effect of an imprecise correction for Galactic
extinction and the effects of contamination by fainter over-lapping objects in
photo-z determination. The overall conclusion of this work is that the
acquisition of photometrically estimated redshifts with the precision required
for Euclid, or other similar experiments, will be challenging but possible.
(abridged)
