  Nuclear reactors provide intense sources of electron antineutrinos,
characterized by few-MeV energy E and unoscillated spectral shape Phi(E).
High-statistics observations of reactor neutrino oscillations over
medium-baseline distances L ~ O(50) km would provide unprecedented
opportunities to probe both the long-wavelength mass-mixing parameters (delta
m^2 and theta_12) and the short-wavelength ones (Delta m^2 and theta_13),
together with the subtle interference effects associated with the neutrino mass
hierarchy (either normal or inverted). In a given experimental setting - here
taken as in the JUNO project for definiteness - the achievable hierarchy
sensitivity and parameter accuracy depend not only on the accumulated
statistics but also on systematic uncertainties, which include (but are not
limited to) the mass-mixing priors and the normalizations of signals and
backgrounds. We examine, in addition, the effect of introducing smooth
deformations of the detector energy scale, E -> E'(E), and of the reactor flux
shape, Phi(E) -> Phi'(E), within reasonable error bands inspired by
state-of-the-art estimates. It turns out that energy-scale and flux-shape
systematics can noticeably affect the performance of a JUNO-like experiment,
both on the hierarchy discrimination and on precision oscillation physics. It
is shown that a significant reduction of the assumed energy-scale and
flux-shape uncertainties (by, say, a factor of 2) would be highly beneficial to
the physics program of medium-baseline reactor projects. Our results also shed
some light on the role of the inverse-beta decay threshold, of geoneutrino
backgrounds, and of matter effects in the analysis of future reactor
oscillation data.
