Can superdeterminism resolve contextuality, entanglement and Shor's algorithm in quantum mechanics? Superdeterminism is the idea that the apparent freedom for the choice of experimental apparatuses and their settings are nothing but an illusion. Contextuality is the dependence of the properties of a system upon the choice of measuring device. However, what if there is no "free" choice of measurement settings, i.e. the measurement settings aren't a freely variable independent degree of freedom? Bell inequalities require counterfactual polarization settings, but what if the polarization setting could only have been one way and not any other? As for the ability of Shor's algorithm to factorize large integers and compute discrete algorithms, maybe the answers gotten at the end retrocausally determine the numbers fed into the quantum computer in the first place so that it couldn't have been any other number?
Are there any absolutely fatal objections?
 A: What would you recognize as an absolutely fatal objection?
Let us brush aside the fact that it more or less is an assumption that experimental physics is doomed to fail to accurately reveal important features of the world and that science is doomed. These consequences make this question a better fit for Philosophy.SE than here; but never mind — let's tackle the philosophical question, and accept that it is entirely conceivable (if not very productive to put into practise) that the enterprise of modern physics is futile.
What we are basically discussing, here, is whether or not conscious human choices are constrained by local hidden variables in such a way, by a deterministic universe, that it tends to give rise to choices of measurements which reveal correlations which seem impossible for local hidden variables; or whether conscious human choices about what numbers we would choose to factor are constrained so that we only choose to factor the numbers which the hidden variables of the quantum system happen to be useful to factor. That is: that our brains — one of the most complicated uncontrolled systems that we know of — either has a vast  supply of secret correlations with the world around us, or is so thoroughly prone to ingress of such secret information, that it serves to constantly thwart any attempt to discover the fact that the world around us is not random, nor involves any apparently non-local effects.
This is Cartesian paranoïa at its finest. In order for a deterministic physics to give rise to conscious agents such as ourselves, and at the same time spoof us with outcomes that seem routinely probabilistic, with reasonable convergence of frequencies of events to reliable averages, by directing us to think that we are choosing to make measurements for which the outcomes seem random but correlated in a way that defies expanation by local hidden variables — this seems to me to require not just a fine-tuned universe hospitable to life à la the anthropic principle, but a cosmological coincidence so enormous as to require an intelligent agency whose purpose is to deceive; to design ants just so that it could poke at anthills. While this position presents a solution to such classic theological conundrums as The Problem of Evil, does it really seem like a simpler hypothesis than just the idea that nature is stochastic, and a just little more complicated than we've ever had reason to believe before 1900 CE?
Consider this, as well: if we manage to build a large quantum computer, there is nothing to prevent us from setting up a computer so that it will multiply each pair of odd primes over 106 in some fixed order, and then re-factor each such product using Shor's algorithm. The only "choices" involved in the running of the computer, then, are the details of the design of the computer, the precise moment when we decide to turn it on, and the mathematical theory (running all the way down to number theory!) which underlies its operation. Failing mysterious failures of the computer, a cosmic conspiracy which tried to fool us into believing quantum mechanics would have to be responsible for the precise moment we turn the computer on, and the entire course of the development of mathematics and engineering leading to Shor's algorithm and the building of the quantum computer, to continue to fool us. Furthermore, these forces which determine our behaviour so precisely must somehow manage to avoid detection, either by making us constitutionally unable to realise that they're going on, or by giving rise to these developments in technology by a sudden cascade of events at the last second, even as our behaviour is being guided in other ways by the same hidden variables. 
There is simply no reason, at present, to consider this a reasonable hypothesis. It is delicate to the extreme, and I cannot even begin to fathom how precisely the initial conditions would have to be tuned in order to make it true — especially in view of the fact that complex systems exhibit such instability that the "cosmic lie" would presumably be quickly revealed unless the initial conditions were set just so. Only someone who was absolutely committed to determinism and local realism, in preference to any sane and pragmatic approach to epistemology or ontology, would ever entertain it. But then, if the world is actually as they describe, we shouldn't blame them for it; after all, they have no more choice to believe it than I have to mention quite tangentially that 11×13 = 143.
A: I am not a scholar of the concept of "superdeterminism" so I may get some historical nuances of the idea wrong. But superdeterminism is just determinism. More precisely, it is a fallacious attempt to find a loophole in Bell's theorem by noticing that determinism, if true, would apply to the experimenter as well as to the experiment.  
Bell inequalities typically pertain to an experiment in which there is some choice about what you measure, e.g. spin up vs spin down, or angle of a polarization filter. Then you look at the statistics predicted by quantum theory, and notice that a local deterministic theory would be unable to produce them, unless the particles had advance knowledge of the measurement settings. There's no reasonable way for them to have that knowledge anyway, but just to make the point, exposition of Bell's theorem may emphasize the ability of the experimenter to choose the measurement settings after the particles (e.g. in an EPR pair) set out towards the measuring device. 
At this point, the "superdeterminist" says "Aha! But if determinism is true, then the experimenter's choice was predetermined, all the way back to the big bang, so in principle the particles had access to information implying what the choice would be." Which is true, but ridiculous. We could set up these experiments so that the settings are controlled by any absurd mechanism you imagine; for example, the total amount of droppings from a mouse in a cage - if it's more than X, we measure spin up, if it's less than X, we measure spin down. 
It is absurd to suppose that the microscopic causality of the universe is such that it would always set the hidden variables inside the particle in a way which matches the amount of droppings that the mouse produces; or equivalently, that the microscopic causality of the universe is always going to finetune the metabolism of the mouse in order to match the hidden variables on board the approaching particle. Yet this really is the sort of thing that the superdeterminist loophole requires! (If anyone has a non-absurd formulation of superdeterminism, I'd like to know about it.) 
Retrocausality, which was also mentioned in the question, is a completely different concept. A retrocausal theory - perhaps we should say bicausal, since it would be "procausal" as well as retrocausal - has two arrows of time in it, going in opposite directions. So it can be locally procausal and locally retrocausal, and still have spacelike correlation and loops in time. But no-one has a working model of such a theory. 
A: Superdeterminism is simply the theory that determinism is predetermined. For that to be true then we are saying that something can only come from nothing thereby establishing true cause and effect. Anything that is 'truly' casual can not exist prior to its own existence. There is only one thing can satisfy such requirements and that is a true causal dichotomy which would be non-local to its effectual state, i.e., spin, which we observe as local. Follow me so far?
If so, then perhaps you will find my findings on this topic of importance:
http://fqxi.org/community/forum/topic/1809
... John Bell was right, "There is a way to escape the inference of superluminal speeds and spooky action at a distance. But it involves absolute determinism in the universe, the complete absence of free will."
