Its just another way to say 'showed,' but puts an emphasis on the importance of a change in facial expression, its very rarely ever used, never in day to day life.

This meaning of "Register" is definitely only used in formal speech and writing. Possible alternatives (in everyday, spoken conversation): 1. Her face showed that she disapproved. 2. Shock could be seen in everyone's face. If you look at a dictionary, almost every definition has the idea of: Recording something with certainty and / or Clearly showing or marking something because of input So, if you want to express a little more certainty than "show," as well as a marked change / reaction / response, you may want to use "register." Both of your sentences give the impression that their expressions probably CHANGED to a certain, clear expression because of something that JUST happened.