  We study the coherent photoproduction of pseudoscalar mesons---particularly
of neutral pions---placing special emphasis on the various sources that put
into question earlier nonrelativistic-impulse-approximation calculations. These
include: final-state interactions, relativistic effects, off-shell ambiguities,
and violations to the impulse approximation. We establish that, while
distortions play an essential role in the modification of the coherent cross
section, the uncertainty in our results due to the various choices of
optical-potential models is relatively small (of at most 30%). By far the
largest uncertainty emerges from the ambiguity in extending the many
on-shell-equivalent representations of the elementary amplitude off the mass
shell. Indeed, relativistic impulse-approximation calculations that include the
same pionic distortions, the same nuclear-structure model, and two sets of
elementary amplitudes that are identical on-shell, lead to variations in the
magnitude of the coherent cross section by up to factors of five. Finally, we
address qualitatively the assumption of locality implicit in most
impulse-approximation treatments, and suggest that the coherent reaction
probes---in addition to the nuclear density---the polarization structure of the
nucleus.
