SPOILERS
I watched both episodes, and I am surprised at my own lack of enthusiasm for this. For a lot of reasons. One, this was a fantastic 90 minutes of sci-fi on TV with production values beyond probably anything we've ever seen in this particular genre, for this particular medium. They spared no expense, except when it came to the story.
Burnham is a fascinating character, and Martin is an outstanding actress, but they fumbled her introduction. A human raised Vulcan is a unique take, and would have provided a lot of interesting conflict. They sped right through it. The show does make bold choices with Burnham, and with the series itself, so all due credit. I feel like they sacrificed character for spectacle in these two hours.
Having written a sci-fi pilot that was consciously a response/reaction to Star Trek, I think I can say a couple things: 1) it's not a good idea to not introduce your primary setting and cast in the first TWO episodes (I tried to be cute with this in my pilot and received pretty universal feedback that it wasn't successful) and 2) you don't spend one or two hours building up characters you then kill. This is a non-starter generally in fiction as in TV and never works (see Doyle on Angel).
Michelle Yeah is as always a treat. Doug Jones and Saru are lots of fun; I liked his 'I really rather wouldn't' attitude. The actor playing Sarek is terrible. Lots of neat details and cinematography. The dialogue was very wooden sometimes, especially in part two.