Non-trivial cases where the frozen core approximation is bad?
The frozen core approximation (FCA) falls apart whenever you need orbital relaxation of the core to accurately describe your system. From a theory-based argument, there are multiple electronic structure methods which rely on this (CCSD, orbital optimized methods) to better account for correlation effects. However, given that the core orbitals do not change appreciably during most processes (ionization, binding, standard chemical reactions), the error introduced by the FCA is all but completely cancelled (you can still get sub kcal/mol accuracy with the FCA).

However, one case where it rears its head is when you're trying to calculate the single-point energy of a system. In this case, the FCA will get in the way of recovering (for example) the full CI result in the full basis set limit.