The current zeitgeist here is on interpretations of quantum mechanics, so let me add my own two cents here. As you may know, consistent histories is an alternative interpretation proposed in a series of papers 1990-1994 by Gell-Mann and Hartle. In a shocking article, Dowker and Kent proved there are many distinct consistent histories for most quantum systems. Even if we constrain ourselves to quasiclassical histories, i.e. those histories which are close to classical, being quasiclassical now does not guarantee being quasiclassical in the future, or in the past. This is disturbing. Do histories which are quasiclassical for all times exist? If they do, are they unique? Is the nightmare scenario of two everywhere quasiclassical consistent histories which are mutually incompatible possible?
Dear Billy, it is not quite clear why you add the emotional words such as "shocking" and "disturbing". It is a manifestation of the essence of quantum mechanics that the classical limit or the spectrum of allowed questions is not God-given. The classical limit occurs in situations that depend on the state of the system as well as its Hamiltonian. The process of decoherence also depends on these two things.
So it shouldn't be surprising that properties that behave classically generally cease to behave classically in the future (or ceased/started in the past). Consider an analogy in statistical physics and thermodynamics. The thermodynamics description works if there are many particles etc. But you may produce lots of new particles e.g. by the LHC proton-proton collisions. Thermodynamics is not applicable to the initial state of 2 particles - too few - but it is useful to describe the quark-gluon plasma and other things that may be formed.
The case of decoherence and consistency of histories is analogous. These things are simply not eternal and God-given. Classical limits only work in some situations, the situations are described by some inequalities involving values of parameters, and because parameters evolve with time, so does the applicability of the classical limit - and so does the consistency of various histories.
It's really a feature of quantum mechanics, not a vice.
Concerning the non-uniqueness, the situations in which the questions are non-unique are unrealistic, but yes, in principle, quantum mechanics allows one to ask different types of questions with different alternative answers that can't be reduced to the same fine-grained set of alternatives. Why do you think it's bad? Again, the right questions depend on the Hamiltonian and the state. They're not God-given. And classical physics isn't a "skeleton" of quantum mechanics that quantum mechanics is only allowed to "slightly disturb". The world is quantum mechanical and quantum mechanics is a qualitatively different description than classical physics, and classical physics is a limit. So classical limit is not a skeleton of quantum physics you may rely upon; it is the sweat on the skin, a derived product that only works on the boundaries of the parameter spaces.
I recommend you a paper by Zurek
that addresses and summarizes many issues. Search for "Dowker" in the paper above. The paper has 1,000+ citations. You will see that there's really no problem in understanding classicality etc.