In the first part of the talk, I will discuss consistency conditions for the applicability of causality constraints in dCS gravity. I will show that after taking the range of validity of the eikonal approximation into account, the possible theoretical constraints are less stringent than the constraint based on astrophysical observations and cannot be used to rule out dCS gravity -- contrary to what has been claimed in the literature. In the second part of the talk, I will revisit some aspects of the dCS classical and quantum symmetries. It has been argued that dCS gravity can be reduced to Einstein gravity after "rotating away" the gravitational-Pontryagin coupling into the phase of the Weinberg operator -- analogous to the rotation of the axion zero-mode into the quark mass matrix. I will show that this is not the case, precisely because of the B-L chiral gravitational anomaly. Then I will introduce a minimal extension of the SM where the coupling of the dCS scalar with right-handed neutrinos induces both the scalar-Pontryagin coupling and an axion-like phase in the dimension-five Weinberg operator at low energies.