In this work, we investigate approaches to leverage self-distillation via predictions consistency on self-supervised monocular depth estimation models. Since per-pixel depth predictions are not equally accurate, we propose a mechanism to filter out unreliable predictions. Moreover, we study representative strategies to enforce consistency between predictions. Our results show that choosing proper filtering and consistency enforcement approaches are key to obtain larger improvements on monocular depth estimation. Our method achieves competitive performance on the KITTI benchmark.