One of the benefits of being the maker of the game is that you get to take some artistic license with interpreting these things. So far, I've seen nothing to complain about Crono's characterization.
Having said that, I'll offer a criticism: Many of the characters in the game seem distractingly similar, personality-wise. That'd probably be the fault of whomever took point on writing the dialogue. One of the tricks to video game characterizations is that you have a very small amount of overall word space in which to get your characters' personalities across, and to do it well you have to be a little exaggerative (or just naturally good at characterization in a minimalist medium, but the other way is easier).
The only "That's not right" moment I've had so far in the game was when Magus got mad at somebody and shouted at them. Unfortunately I don't remember the line. I think it was "You'll pay for that!" or something similar.
