With the setup in this video: http://www.youtube.com/watch?v=YVms3avJ79Y
You are able to delete and duplicate blocks, when placing it on the pulsing sticky piston. The duplicated block however is some kind of ghost block, since it can't be mined (does not drop an item), will disappear when updated or when the world is reloaded.
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Seems to only duplicate client side - not a massive issue, but definitely confusing visually.
However I am able to stand on these duplicated blocks. But Mobs do not seems to be able to stand on them.
Sounds like a duplicate of MC-151, please let me know if I'm wrong. 😉
It does seems to be the same as is shown in this video: http://youtu.be/FTcL0HnY24U commented by "tyson h", however he says "not really the same thing but it's still the bug in a way", so I am not sure whether this is the same bug or not.
Here is a more in depth video I found on YouTube which displays and explains this glitch even more: http://www.youtube.com/watch?v=Zb8iFoVnKGQ
Confirmed in 1.4.7.
You should vote for this bug if you want it to get fixed soon. Another example: http://imgur.com/a/VmGKh
Confirmed in 13w10a, Another example.
http://youtu.be/HSycrzaF4rc

Is this still a concern in the current Minecraft version? If so, please update the affected versions in order to best aid Mojang ensuring bugs are still valid in the latest releases/pre-releases. If this has been done, we can reopen the issue.
Keep in mind that the "Resolved"-Status on this ticket just means "Answered", and that we are waiting for further information on whether this issue still exists or not. We will reopen it as soon as the requested information has been deliviered.
I'm seeing this in the 1.9 Release (not snapshot). Sticky Pistons (hooked up to an armor stand timer with soul sand) are duplicating Chiseled Stone, and pushing out the duplicates.
Logging out of the server and back in will reset it, so it still appears to be client side.
See MC-96219.

Still an issue in 1.11.2, please reopen.
As you can see from the attached screenshot this is not just a visual glitch. Although the blocks cannot be mined, you can stand on them and cannot move through them.
@unknown, that would be MC-54026.