This is not a question, let's list down all the effects resulting from breaking or preserving of various discrete symmetries, on various observables, be it in condensed matter or in high energy. Please discuss the subtleties, if there are any.
Some examples would be:
- The off-diagonal elements of conductivity are finite if T-symmetry is broken, otherwise it's zero.
- Breaking chiral symmetry gives rise to mass (apart from Higg's mechanism).
- Breaking inversion symmetry gives rise to Rashba (spin-orbit coupling) effect.