  The expected gamma-ray flux coming from dark matter annihilation in dwarf
spheroidal (dSph) galaxies depends on the so-called `J-factor', the integral of
the squared dark matter density along the line-of-sight. We examine the degree
to which estimates of J are sensitive to contamination (by foreground Milky Way
stars and stellar streams) of the stellar-kinematic samples that are used to
infer dark matter densities in `ultrafaint' dSphs. Applying standard kinematic
analyses to hundreds of mock data sets that include varying levels of
contamination, we find that mis-classified contaminants can cause J-factors to
be overestimated by orders of magnitude. Stellar-kinematic data sets for which
we obtain such biased estimates tend 1) to include relatively large fractions
of stars with ambiguous membership status, and 2) to give estimates for J that
are sensitive to specific choices about how to weight and/or to exclude stars
with ambiguous status. Comparing publicly-available stellar-kinematic samples
for the nearby dSphs Reticulum~II and Segue~I, we find that only the latter
displays both of these characteristics. Estimates of Segue~I's J-factor should
therefore be regarded with a larger degree of caution when planning and
interpreting gamma-ray observations. Moreover, robust interpretations regarding
dark matter annihilation in dSph galaxies in general will require explicit
examination of how interlopers might affect the inferred dark matter density
profile.
