Do I need to replace this bathroom tile backing

Found some water leaking into a room adjacent to the bathtub and found it was coming through a loose bathtub tile (or two). I removed several of them and this is what I see. Can I just re-tile, or will I need to rip it all out and use cement board backing. Hoping to avoid a big job here, but also don't want something that will fail quickly. Thanks, you all are the best :)







Full size image here: https://dl.dropboxusercontent.com/u/...hrubtiling.jpg



Also, a few other tiles have hairline cracks in them, do they need to be replaced as well? Thanks!