  The ability to constrain dark energy from the evolution of galaxy cluster
counts is limited by the imperfect knowledge of cluster redshifts. Ongoing and
upcoming surveys will mostly rely on redshifts estimated from broad-band
photometry (photo-z's). For a Gaussian distribution for the cluster photo-z
errors and a high cluster yield cosmology defined by the WMAP 1 year results,
the photo-z bias and scatter needs to be known better than 0.003 and 0.03,
respectively, in order not to degrade dark energy constrains by more than 10%
for a survey with specifications similar to the South Pole Telescope. Smaller
surveys and cosmologies with lower cluster yields produce weaker photo-z
requirements, though relative to worse baseline constraints. Comparable photo-z
requirements are necessary in order to employ self-calibration techniques when
solving for dark energy and observable-mass parameters simultaneously. On the
other hand, self-calibration in combination with external mass inferences helps
reduce photo-z requirements and provides important consistency checks for
future cluster surveys. In our fiducial model, training sets with spectroscopic
redshifts for ~5%-15% of the detected clusters are required in order to keep
degradations in the dark energy equation of state lower than 20%.
