  Dwarf spheroidal (dSph) galaxies are among the most promising targets for the
indirect detection of dark matter (DM) from annihilation and/or decay products.
Empirical estimates of their DM content - and hence the magnitudes of expected
signals - rely on inferences from stellar-kinematic data. However, various
kinematic analyses can give different results and it is not obvious which are
most reliable. Using extensive sets of mock data of various sizes (mimicking
'ultra-faint' and 'classical' dSphs) and an MCMC engine, here we investigate
biases, uncertainties, and limitations of analyses based on parametric
solutions to the spherical Jeans equation. For a variety of functional forms
for the tracer and DM density profiles, as well as the orbital anisotropy
profile, we examine reliability of estimates for the astrophysical J- and
D-factors for annihilation and decay, respectively. For large (N > 1000)
stellar-kinematic samples typical of 'classical' dSphs, errors tend to be
dominated by systematics, which can be reduced through the use of sufficiently
general and flexible functional forms. For small (N < 100) samples typical of
'ultrafaints', statistical uncertainties tend to dominate systematic errors and
flexible models are less necessary. We define an optimal strategy that would
mitigate sensitivity to priors and other aspects of analyses based on the
spherical Jeans equation. We also find that the assumption of spherical
symmetry can bias estimates of J (with the 95% credibility intervals not
encompassing the true J-factor) when the object is mildly triaxial (axis ratios
b/a = 0.8, c/a = 0.6). A concluding table summarises the typical error budget
and biases for the different sample sizes considered.
