The objective of this work is to automatically produce radiological gradings of spinal lumbar MRIs and also localize the predicted pathologies. We show that this can be achieved via a Convolutional Neural Network (CNN) framework that takes intervertebral disc volumes as inputs and is trained only on disc-specific class labels. Our contributions are: (i) a CNN architecture that predicts multiple gradings at once, and we propose variants of the architecture including using 3D convolutions; (ii) showing that this architecture can be trained using a multi-task loss function without requiring segmentation level annotation; and (iii) a localization method that clearly shows pathological regions in the disc volumes. We compare three visualization methods for the localization. The network is applied to a large corpus of MRI T2 sagittal spinal MRIs (using a standard clinical scan protocol) acquired from multiple machines, and is used to automatically compute disk and vertebra gradings for each MRI. These are: Pfirrmann grading, disc narrowing, upper/lower endplate defects, upper/lower marrow changes, spondylolisthesis, and central canal stenosis. We report near human performances across the eight gradings, and also visualize the evidence for these gradings localized on the original scans.