In computational chemistry, it is extremely common to freeze the core electrons after an initial Hartree-Fock calculation, meaning that the core electrons are left out of any treatment of the electron correlation. Which orbitals are considered core depends on the atom, but for the second row, it usually just means the 1s electrons are not correlated.
This is an intuitive approximation, as one would expect that correlation of the valence electrons would have the greatest effect on any actual chemistry.
Now, clearly one can imagine situations where freezing the core electrons is a very bad idea. One such case is if you were interested in modelling x-ray spectroscopy. I am less interested in this type of example as this is almost just a user error, and hence I would consider this a somewhat trivial example.
So, to be concrete, are there any known examples in which treatment of correlation of the core electrons results in a qualitative change in the modelling of a process which is primarily mediated by the valence electrons?
My guess is if there is an example it occurs in the third row and beyond.