When does $\hbar \rightarrow 0$ provide a valid transition from quantum to classcial mechanics? When and why does it fail?

The theory of deformation quantization provides a framework in which the quantum to classical transition can be carried out and understood.

According to this theory, for (practically any) quantum system, one can find (may be nonuniquely) a Poisson manifold $\mathcal{M}$ (phase space) equipped with an associative product called the "star product" such that the quantum observables are represented by smooth functions on $\mathcal{M}$ and the quantum operator product is given by the star product.

Furthermore, the star product of two functions has a formal power series in $\hbar$

$f\star g = \sum_{k=0}^{\infty} \hbar^k B_k(f,g)$

Such that:

$B_0(f,g) = fg$

$B_1(f,g)-B_1(g, f) = \{f,g\}$, (Poisson bracket)

Thus we obtain:

$f\star g - g\star f = \hbar\{f,g\} + \sum_{k=2}^{\infty} \hbar^k (B_k(f,g)-B_k(g,f))$

Please notice that according to the deformation Philosophy, the quantum observables are just functions on the phase space just as the classical observables and all the quantum noncommutativity is provided by the star product. Thus if we define $\hat{f} = \frac{\hbar}{i} f $, we get the required classical limit.

It should be emphasized that this procedure can be carried out even for quantum systems defined by matrix algebras for example an appropriate phase for spin iis the two-sphere $S^2$, please, see the following article by Moreno and Ortega-Navarro. Morover,

Kontsevich in his seminal work provided a constructive method to construct this star product on every finite dimensional Poisson manifold, Please see the following Wikipedia page.

It is also worthwhile to mention that there are efforts to generalize the deformation construction to field theories and incorporate renormalization into it, please see the following work by Dito.

This sounds reasonable.

My rather rough understanding is that, (if there is a classical action for the transition,) in the limit it is only the neighbourhood of the classical action that is contributing. The contribution of the classical action itself maintains to have measure $0$ relative to the contribution of the neighbourhood, even when taking the limit (wherein that neighbourhood goes to "size" or "spread" $0$.)

If there isn't a classical action for the transition, then the whole thing fails anyway.