Have watched all the eps so far.
Burnham is terribly cast. The character acts nothing like a supposed Vulcan would, with regular sarcastic or snarky comments that are completely out of character for what I believe Vulcans are meant to be.
Captain is well cast and well done; he's bombastic and sure of himself and defies orders regularly.
Redhead is ok, but I have no idea what her role is on the show. She doesn't advance anything or have any particular character motivation.
As for the latest episode, what is the supposed reason that Stamets cannot get the new security guy to help him? The whole thing seems ridiculously forced, and the "secret" that Burnham tells Stamets is outlandish in terms of being something that she would certainly believe him in future time loop iterations.
As well, I find it a little difficult to believe that..