There are also papers from the 80's by Itamar Pitowsky on hidden variables models using nonmeasurable sets.
http://edelstein.huji.ac.il/staff/pitowsky/ (papers #1 and #4 for example)
For the Kochen-Specker theorems there is a long line of later results but see especially the Conway-Kochen "Free Will Theorem", available on arxiv (quant-ph).
I don't think physicists take seriously the idea that set theory is (or even might be) relevant to quantum mechanics. On the mathematical side the set-theoretic models can be seen as demonstrations that certain types of hidden variable models are logically consistent, and so cannot be ruled out without additional assumptions, such as Lebesgue measurability, that are implicit in ordinary physics reasoning.