Steps to Reproduce:
-Have the host open a world.
-Join the host's world as the client.
-As the client make this structure (should be 3 blocks in height)
http://i.imgur.com/UlXtNQa.jpg -step 1
http://i.imgur.com/MPp1bbO.jpg - step 2
http://i.imgur.com/5xbD1yI.jpg - step 3
http://i.imgur.com/wieLQoK.jpg - step 4
http://i.imgur.com/LOvi70u.png - step 5

Conclusion:
What the client sees
http://i.imgur.com/Q5ZGZ0R.png
What the host sees
http://i.imgur.com/sUfeYhk.png

The host can break the block and a new cobblestone block is generated again. However the client cannot mine the cobblestone since the only thing the client will see is lava sitting next to water that did not mix to form a block.

In case your wondering, what you just made is a cobblestone generator. I among others would appreciate it if this bug was fixed. This is be the best way I could describe the issue.