In my world there are some chunks that are completely empty, down to the (missing) bedrock. We can build inside them, making bridges, but falling into them results in death ("Player has fallen outside the world" or something similar).
As visible in the screenshot water from adjacent chunks doesn't fall of, but if we place water near the border it does fall. 
On the map these chunk are shown as completely black.

I think the server may have shut down unexpectedly, possibly corrupting some files, but unfortunately i can't be 100% sure of what happened, since we found the problem exploring after the world was moved around.

If anyone has any idea how to fix those chunks (forcing them to be rebuilt?) it would be greatly appreciated.