We study the use of error-correction coding (ECC) and two-dimensional interleaving for volume holographic memory (VHM) systems suffering from both random and systematic errors. The bit-error rate (BER) is used as the data-fidelity measure and as a design metric for optical 4f systems. The correlated error patterns arising from both lens aberrations and misalignment errors are analyzed, and we discuss the information theoretic storage capacity of VHM in the presence of such correlated error patterns. The performance of interleaving and ECC is analyzed from both BER and storage-capacity perspectives. Magnification, rotation, tilt, and defocus errors are also studied, and an experimental demonstration that combines ECC with two-dimensional interleaving is included.