  The cosmological constant and many other possible origins for acceleration of
the cosmic expansion possess variations in the dark energy properties slow on
the Hubble time scale. Given that models with more rapid variation, or even
phase transitions, are possible though, we examine the fineness in redshift
with which cosmological probes can realistically be employed, and what
constraints this could impose on dark energy behavior. In particular, we
discuss various aspects of baryon acoustic oscillations, and their use to
measure the Hubble parameter H(z). We find that currently considered
cosmological probes have an innate resolution no finer than Delta z=0.2-0.3.
