We apply advanced X-ray diffraction techniques at synchrotron microfocus beamlines in order to study the local ultrastructure of biogenic calcite with high spatial and angular resolution. Specifically, we investigate individual calcitic prisms extracted from Pinna nobilis mollusk shells with an aim to shed additional light on the structural aspects of organic/inorganic interfaces. We use annealing at elevated temperatures to destroy intracrystalline organics and measure the same prisms before and after annealing to achieve deeper understanding of the internal organization of these nanobiocomposites. Complementary nanoindentation measurements (also performed before and after annealing) allow us to elucidate the role of intracrystalline organics in increased hardness in pristine prisms and hardness reduction after annealing. We found that removal of intracrystalline organics during annealing facilitates generation of well-oriented lattice defects, which reduce the (006) diffraction intensity and are responsible for the [001]-elongated diffuse streaks nearby diffraction spots. These findings indicate the formation of internal material's discontinuities with smooth and flat interfaces. Such nanodiscontinuities facilitate microcrack propagation under load that explains the reduced hardness of calcitic prisms after annealing.