I know this is a very general question, but I'm hoping someone well-versed in quantum theory is willing to provide an (appropriately general) answer.

Whilst investigating unrelated matters today I ran into a, "Brief Introduction to Consistent (Decoherent) Histories" which read (in part):

The above makes such an interpretation sound like a silver bullet against the ambiguities that appear pandemic to these kinds of discussions. From what little I've gathered on the topic (just in the course of other inquiries), I thought rigorously defining such histories (and identifying when decoherence takes over, etc.) was not[/] a trivial task. Can anyone tell me what the quoted author has left out, or the thinking behind such a rosy picture?

There is no catch - like any interpretation on its own terms it resolves the issues. The basic problem is do you like its terms? To me (and I have to say CH is one of my favorite interpretations) its defining your way out of problems.

You're right, from that description you might think like consistent histories has little in the way of downsides. Here's an aesthetically undesirable (at least for me) feature of consistent histories, taken from the website you linked to:

That's true. However my concern is the idea indeterminism is somehow objectively ugly - it aren't - any more than determinism is or isn't. That's simply a reaction some have when exposed to the theory and has nothing to do with its validity. I personally find a probabilistic theory very beautiful since it is more general than determinism which only allows probabilities of 0 and 1.

All interpretations have appealing features to some and sucks to others - that's why a consensus has never nor it is doubtful will ever be reached.

I have read a number of papers and books on Consistent Histories and they are all well written and argued. For an introduction to the mine field of interpretation you can do a lot worse.

Bhobba, I disagree.
Indeterminism is immensly ugly philosophically.

Why would any sort of indeterminism follow a statistical law (Born rule) ? That needs explanation (cause) and then we are back at determinism. But no, people like that want to believe that the universe magically CHOOSE free willingly to follow a statistical law.
It makes absolutely no sense whatsoever.

In the history of science, determinism has ALWAYS triumphed and I would be genuinely shocked if it does not happen in QM too.
For me indeterminism is as likely as solipsism.

And every philosopher would agree with that? If so it would be a first.

Well lets see shall we. Suppose we have some kind of observational apparatus with n possible outcomes. We have two possibilities - knowing everything about the system allows us to predict with certainty the outcome of the observation or it does not. If it does not then its quite reasonable the proportion of any outcome approaches a stable limit after a large number of trials in which case we have probabilities. If not then all hope is lost of actually making any kind of prediction. So what you are saying is why should nature allow us to at least make probabilistic predictions. Gee mate I don't know - but I am glad it does considering the alternative.

As to why the Born rule - check out Gleason's theorem: http://en.wikipedia.org/wiki/Gleason's_theorem
'Gleason's theorem therefore seems to hint that quantum theory represents a deep and fundamental departure from the classical way of looking at the world, and that this departure is logical, not interpretational, in nature.'

Although as Von Neumann noted in his proof of no hidden variables it also follows from the additivity of expectation values. Basicall this is very simple - if the average outcome of observable A is <A> and observable B is <B> then the average outcome of observable A + B is <A> + <B>. With that assumption Born's rule follows. But as Bell and others showed that assumption is not necessarily true for hidden variable theories. But still such additivity is a very very reasonable assumption - so reasonable it took a long time for it to be questioned.

Basically its the most reasonable probabilistic theory that allows continuous transformations between pure states.

And why would nature care how likely you think something is?

Seriously though opinions are like bums and based on all sorts of things such as aesthetic sensibility, but while its important to hold opinions it does not make them correct. That applies very much to me and I would suggest to views like you expressed as well.

Thanks to everyone for the replies (I did not check back since the original posting). I'm getting that CH theories don't made definite predictions about the future, and that although they can say what sets of measurement/events fit together (in a history), they won't say WHICH one will be the "real" one?