When placed at certain coordinates within a world, droppers and dispensers do not consistently activate when powered by redstone wire from a block above (see attached screenshot for setup).

After it has been first set up, or after block updates to the redstone/surrounding blocks are made, the dropper will work once, but subsequent powerings of the redstone will fail to activate the dropper.

This bug affects droppers/dispensers depending on where they are located in the world. In  the image (and worldsave) I have attached, the two dropper setups are identical, but only the one on the right works as it should. The dropper on the left is affected by the bug. 

The specific coordinates where this bug occurs differs from world to world: I tested using the same seed multiple times and often the broken droppers occurred at different locations.
However, the locations where the bug occurs remain constant in any one world (ie. the dropper on the left in my worldsave will consistently be broken as long as it is on that spot, even after rebuilding it)

I have not noticed a pattern as to where these bugged blocks occur within a world - they seem to be random but it is very common - by repeatedly recreating the identical dropper setup shown in my image across different blocks in your world you will soon encounter the problem.