I see the score at the end of the game, but in the menu is a way to see scores for individual characters. However, I have not seen those scores ever updated. Are they not used yet?

Yeah, I see the same thing, you get to enter a name and if you do it replaces the investigator list, keep entering more and more lost. Win or lose, the investigators don't seem to have their scores tracked (which would be great).

It seems really wonky/faulty.

I should add, that's the only bad thing I see in the app, otherwise great fun.