The pictures describe this better, but in words: when a carpet is placed on a block that is pushed away by a sticky piston, the carpet will remain on the extended rod of the piston. When the piston is retracted, the carpet breaks while the piston is retracting. This should not happen, because there is a block under the carpet at all times.
This may sound like a duplicate of MC-17851, but it is actually a bit of a different scenario, so i decided to open a new issue for it.
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technially that is still a block. This probably can also be considered a duplicate to MC-17851
I dont think it is a duplicate, since those issues are about pushing and pulling the carpet itself. This issue is about a carpet that should stay where it is placed, while stuff beneath it is happening.
edit: fixed a typo
you may be right on that, seem to rememebr this issue somewhere else though... maybe with signs on a block being moved by a piston. Either way it is doing something that it probably shouldnt be.
Confirmed.
you are right, the exact same thing happens with a sign instead of a carpet.

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.
Yes, the bug is still present in the current version (1.6.2). I added it to the "Affects version/s" field.
carpets are blocks that can be placed on anything except air so when the piston retracks there is no block under the carpet
@Lars Kikkert: You would be correct if this would be a normal piston. But in the description of this bug i make clear that i use a sticky piston. While retracting the sticky piston, it pulls the block in front of its rod. Therefore there is never an air block underneath the carpet and it should not break.
@why do you need this? if a piston retracks there is a short moment of no block under it because normal blocks cant move, its just very simple this is not a bug but a misunderstanding
and the reason why it doesnt happen when it pushes it uses the place-holder
@Lars Kikkert: While that may be a technical explanation for this bug, it still is a bug. Stating the cause of the bug does not make it any less of a bug 😉. The carpet stays in place while the piston is extending, so in my opinion it is very reasonable to expect it to stay in place while the piston is retracting.
edit: typo
@why do you need this? then they should make the time for despawning carpet a lot longer and that can cause problems ingame
@Lars Kikkert: with all due respect, but I think you are not a Minecraft developer. This is not the place to discuss how bugs should be fixed, but the place where community members can report issues to Mojang. I think it is rather speculative to say that your proposed solution "can cause problems in-game": we should leave the actual solving to the people who develop Minecraft. I think you can agree with me that the current situation creates an undesirable asymmetry (retracting the sticky piston does break the carpet, while extending it does not) and that this asymmetry should be removed. How and when this issue will be resolved is up to the developers.
@Lars Kikkert - while this may be a "misunderstanding" it can easily be assumed that the (quoting you) "place holder" that is present when the piston extends should be there when it retracks. No extra time delay would be needed, just the code telling the blocks that there is a place holder for the carpet block to still be attached to on piston retrack.
@ Lars Kikkert & @why do you need this? - Calm down guys... we can all agree that this is an apparent bug of some sort whether it be because of programing or just simple user expectations. Let us stop this "discussion" and allow the Mojang guys determine whether or not this gets updated/fixed and to how long it takes them to do so.
@Th3F4114n0n3: No worries, we're calm 😉. I agree, lets wait and see what the devs have to say about this.

Guys please stop arguing. You aren't helping anything.
I'd say the solution would be that it just can't be placed on the piston rod
@Dylan Rivers: That would be a bummer, personally I have use for placing carpets on the side of piston rods. I hope the decision will be to prevent the breaking rather than removing the possibility to place them.
@Ezekiel: I do not see any arguing, just a discussion about this particular issue? If any of my comments sound like I am trying to start an argument I apologize, but please please don't interpret them that way when there is no reason to. Let's keep the discussion on the subject.
@Ezekiel just a question: if you needed to solve it within a minute what would your plan be?

If you have played with redstone, you will know that its not the action of the blocks moving (as seen above), it is most likely just a check happening the second time around causing it to break.
Therefor I would remove this.
I just updated the affected versions with 1.6.4 and 1.7.2, since this bug is not fixed yet.

Considering we were specifically and purposefully given the ability to place carpet on anything, it stands to reason it should be able to stay on piston heads. However, this does deal with action of the piston head, so it's not as straightforward.
Confirmed for 1.7.5 and 14w11b
Confirmed for 14w17a
Confirmed for 14w18

Confirmed for
15w36d However now it also breaks when the block below it changes from a block to the piston arm
WAI per MC-5621.

How is this WAI? MC-5621 was supposed to be fixed but is apparently not
@unknown make sure you have doTileDrops to true

Sorry I could have said that more in detail and was confused as well.
They do indeed drop items, but only when they are pulled back, not when they are pushed.
I think "drop" in this context refers to the block popping off.

I meant it the same way, but it seems that only when the piston pulls a block back the block above it will drop, not if the block below it is pushed
So, umm, do we need to do anything with this ticket?

I don't know maybe MC-5621 needs to be reopened then
Cannot reproduce that ticket in 16w02a.