What criteria distinguishes causality from retrocausality? The brilliant philosopher David Hume remarked that if two events are always found to be correlated to each other with one event happening prior to the other, we call the earlier event the cause and the latter event the effect. However, it has been pointed out that two events can be correlated, with one happening after the other, but only because they both have the same common cause, and not because of any direct causation. It's not "post hoc, ergo propter hoc".
What stops me from defining a new verb "retrocause"? It works just like Hume's definition, but only in reverse. We note the presence of a broken egg is always correlated perfectly (or very very nearly so up to an exponential degree of accuracy. Loschmidt reversal, anyone?) with the existence of an unbroken egg in its past. So, we say broken eggs retrocause unbroken eggs. In the same manner, unbroken eggs retrocause hens laying eggs. And hens retrocause female chicks. And female chicks retrocause hatching eggs. And so on and so forth.
In delayed choice experiments, what stops us from saying the choice of apparatus settings retrocause the preferred basis of a quantum system in its past?
What distinguishes causality from retrocausality?
 A: Another brilliant philosopher, Immanuel Kant claimed that causality, like space and time, are not intrinsic properties of things-in-themselves, nature as it "really" is, as much as they are properties of the observing mind. It is the mind which determines causality, and the mind can be easily fooled.
A: What distinguishes causality from retrocausality?  The laws of physics are pretty much time-symmetric so it seems the two should be not too different.  However, we all know that causality goes from past to future.  This is a question that many have worked on and none have fully resolved.  For an overview, there are a couple of pages on Wikipedia: Arrow of time and Entropy (arrow of time).  It seems the best answer so far is "it has something to do with entropy."
A: Addressing delayed choice (focusing on quantum phenomena):
My simplified view is that setup of the apparatus (and other devices on the path) limits possible properties and paths of photons that may reach it, but, the photon (travelling @ c), makes the whole journey from emission to absorption (detection, collapse) in the very definition of an instant, even if we (incorrectly?) think of it as travelling for thousands of years.
It is then this subjective view of time that makes us prefix retro- to cause.

If this interpretation is accurate (mind the topic still confuses me), the term cause should be disused for quantum phenomena (replaced with interaction). For classical physics, retrocause is an oxymoron (use passive verb).
A: A set of events are called causes for an effect if they're sufficient for that effect to exist. This doesn't imply that the existence of this effect is sufficient for the same set of causes to exist. So whereas causality is consistent with the world we're living in, your idea of retrocausality isn't.
A: The central concept lies in the concept of "independent variables" and "dependent variables". Independent variables are those which can be "freely" varied, while the value of dependent variables are determined by those of the independent variables. What does "can be freely varied mean"? Can't we invert the roles of independent and dependent variables, invert the function, so to speak? And what do we mean by determine? Do we mean determine uniquely, or only determining a probability distribution? Do we need to include all the controlling factors to make it a unique determination? If only a probability distribution, what is the meaning of probability? Maybe what looks like probabilistic randomness is only pseudorandom deterministic or ignorance? Unless our model of causality is fully deterministic in the sense of a unique determination, what looks like a fully determined probability distribution can always be due to some other factors.
Monte Carlo simulations using pseudorandom generators. Do we say the pseudorandom numbers are independent variables?
Bell entangled particles. Measure a spin there, measure a spin here. In rest frame, there first, but still spacelike. Local Copenhagenist will tell you measurement causes the spin outcome, and the probability for its collapse. Nonlocal hidden variable guy says the apparent randomness of the measured spin here is really because we have not accounted for the value of the spin there. Once we do, what looks like randomness is fully determined by superluminal effects which in a boosted frame becomes retrosuperluminal effects. Another hidden variables guy tells you, all was determined causally and nonsuperluminally when the entangled pair was created in the same place, and the Stern-Gerlach orientation was also superdetermined. It appears the orientation is an independent variable which can be freely varied, and is one of the causes, but it's not really. Retrocausalists will tell you the orientation now retrocausally determines the spin basis during creation.
Your example. Maybe in future, 3D printing of female chicks become possible. Then, you can't say female chicks retrocause hatching eggs. Change that to female chicks and no advanced 3D printing technology retrocause hatching eggs? Qualifiers. Maybe the world is a stage and the apparent absence of 3D printers is only an illusion? Backstage, behind the scenes, a director 3D printed a female chick and planted it in your set when you weren't looking. 
Problem of induction. Just because event A always led to event B in its future does not mean it will do so again the next time round.
A: If it's possible to vary the "cause" "freely" while keeping all the other "controlling" degrees of freedom fixed, i.e. controlling for all the other factors, and such a variation leads to a change in the outcome of the "effect", that is causality. The problem lies in the choice of what to consider the other controlling degrees of freedom.
Suppose P,Q and R are three propositions taking on true/false values. Suppose R = P XOR Q. Pick Q as the controlling variable. Then, P causes R, but also, R causes P! Pick P as the controlling variable. Then, Q causes R and R causes Q. Now try picking R as the controlling variable. Do you now understand why people refer to the tangled wed of causality?
The existence of intelligent lifeforms, and the very long time it takes for such lifeforms to evolve retrocaused the fine-tuning of the cosmological constant up to $10^{-123}$, and also the need for structure formation which retrocaused slow roll inflation. The existence of carbon based lifeforms retrocaused the carbon nuclear resonance needed for stellar nucleosynthesis. The existence of heavy elements retrocaused the difference of the neutron mass from the sum of electron and proton masses needed for neutrinos to blow off the heavier elements in nova explosions.
A: Here is the correct definition for causality: something is considered a cause of a given event if for any predictor wanting to predict the outcome of that event, whether by reasoning, calculation, simulation, or some other means, that predictor has to include some sort of encoding of the cause, and the entire causal chain emanating from it right till the event, somewhere in the intermediate states of the predictor. 
It might turn out there might not be any correlations between the cause and effect at all. For instance, the outcome of the effect might turn out to be the same whatever the cause is. But if the only way for any predictor to figure that fact out is to actually run many simulations with different values for the cause, and only then note the effect remains the same in each case, it is still safe to say there is a causal relation. The time ordering between the cause and effect does not show up in this definition.
Similarly, there is no need for the cause to be able to be freely varied. Even if the cause can only be the way it is and no other, if any predictor has to include the cause in order to predict, it is still a cause. For instance, suppose all proofs of a mathematical theorem requires invoking a certain crucial lemma. The truth of the lemma is a mathematical fact which can't be varied. Still, it is correct to remark the lemma caused the theorem to be true.
In order to predict that an egg will smash when it falls on the floor at a high enough speed, it isn't necessary to know that a hen laid it. So, that doesn't count as a cause. Similarly, to predict that an egg is going to fall doesn't require any knowledge that it will smash in the future either. To predict the behavior of a chick might require some knowledge of the biology and psychology of chicks, but it doesn't necessarily require any knowledge of the neuroanatomy of its brain, or the detailed anatomy of the chick.
If the best the predictor can do is to give a probability distribution for the event outcomes, that still always leaves room for hidden causes overlooked by the predictor under the guise of apparent randomness.
A: The problem with most of the definitions of causality given here is according to them, if I have a certain memory or record that a certain event happened in this particular manner in my past, my memory of it retrocaused that event to be that way.
I would be interested to know if there is any definition of causality not explicitly mentioning time ordering which rules out this as an example of retrocausality.
A: There is no difference between causality and retro-causality (i.e. all causality is retro-causality and all retro-causality is causality).
For example: Causality can be understood like a wave-function of light - because light is a mechanism of causality. All mechanisms of causality are interacting all the time at every point of time. The wave function then collapses, to what is most probable, at any moment, upon interaction with matter and gravity. For each moment that matter and gravity dictate probability, it effects the wave function at more and more points of interaction.
This results in a temporal continuity where logic systems can exist and interact in an orderly fashion.
A: I don't see any problem at all with your definition of retrocausality.  After all, it's just a definition...  So your first question is moot.
The difference between causality and retrocausality is the parameter time.  On the quantum scale we do use equations such that time moves backward to describe certain interactions.  However, on the larger scale these many interactions form a system where time moves forward (i.e. positive) not backward (negative).  Thus we tend to use causality, not retrocausality.
