I think the acting has been very good.
As for characters, I think they have been mainly good, some great -- but there are two characters that I think need tweaking (and that's no fault of the actors playing the role, but rather the writers).
First, I think Burnham needs to lose the attitude of: "Every problem I see I'll make it my own mission to fix it on my own, and will feel personally responsible to see it through by myself".
It's been discussed to death already that she's not a "Mary Sue", but I can see why some people argue that she is, because she seems to feel she is the only person who can bear the weight of the world, and feels she must do it herself. That's fine as the beginning of a character's journey and growth, but the writers really need to have her finally grow past that feeling. It makes for an isolation of that character from the other characters, and in turn a dull show because the best part of most TV shows -- the chatacrer interactions -- is missing.
Secondly: Stamets. Anthony Rapp is fantastic, but the character seems to have had little to do other than lament the loss of Culber (first physically, now emotionally). We really don't get enough of that "slighty prickly" character we got in the first few episode last season.
I liked that Stamets; he was a bit McCoy-like in that Stamets wasn't afraid to speak his mind about things being done a certain way, but he still had a warmth to him, even when he was being prickly. We get glimpses every so often of that Stamets, such as when we told Tilly she will become a magnificent captain one day, but talks too much. Or recently when he said that Spock and Burnham's debating was helping him work, but a few minutes later told them he changed his mind, and realized their discussion was distracting.
We need more of that Stamets, rather than too much of the brooding aimless one.
