Ooooh, good question. I certainly didn't think of asking that when I first started. I wish I had, after a few years in the hobby and reading about some scary stuff that you can pick up.
Like Bertoni said, those are the most notable deseases...and then you have to watch out for stings from corals, and bristle worms and fire worms and such.... The list is long, so get yourself a good pair of gloves.