I watched this episode on You Tube, courtesy of CBS (thanks to them for them for making the premiere free). I thought it was a solid premiere, but not spectacular. Though I don't think it was meant to be. It was like a set up episode, mostly putting characters and plotlines in place, and that made the episode feel a little aimless. Once they got to the Hiawatha the story felt like it was solidifying if it never quite fully gelled. Once again, the special effects were great.
A lot of the episode was for setting up Anson Mount as Pike and I thought Mount did a fine job. He made a very good first impression and if they keep it up he might become one of my favorite Trek captains. Mount's Pike is not the depressed, hard man from "The Cage", and felt more like Bruce Greenwood's take on the character, though not quite as weathered. I do think at times the show went a little too far in having him differentiate himself from Lorca; at times he felt a little too deferential and not authoritative, though it would make sense that he's being very careful with this crew since their morale must be reeling due to Lorca's betrayal, being stuck in the Mirror Universe, and the other things they've gone through in the last year.
I saw some online criticism about Burnham upbraiding Pike and I didn't get that. She didn't hold her tongue at times, but it didn't feel disrespectful, and Pike also made his points as well. That being said, I do think when it comes to the junior officers, including new character Jett Reno, they could stand to be a little more respectful of the chain of command, or that Pike (or whoever would be the captain/authority) could remind them. I don't see Picard, Janeway, Kirk, Sisko, or even Archer not more firmly asserting their authority. I watched "The Cage" after "Brother" and that Pike definitely would not have. (And with all that being said, I did like how Pike gave up the seat to Saru when it came to a job not that didn't concern investigating the Red Angel; that was very big of him. I also liked his roll call. I thought his going over his service record was a bit too much, however it provided fans some nice nuggets).
I liked the Enterprise security officer and I hope her role gets expanded. Though I also hope we get some nods to the Early Voyages comic, which I really liked. I liked what we got to see of the Enterprise, though I didn't care that it set out the war. And the ship looked pretty alright for it to supposedly be unable to finish the job. I wish they had written it where Discovery comes across a wrecked Enterprise.
I'm not a big fan of the Michael-Spock thing so far. I didn't buy that Spock would've talked about Burnham to Pike. Spock seemed pretty reserved when it came to his personal life so I don't see him just going into something like. Granted, we don't have much to go on when it comes to canon and the Spock and Pike relationship previously and "The Cage" Spock did seem a little more emotional than what I'm used to, but still, it just doesn't feel in character that he would talk about Burnham (though perhaps there was a professional reason for it. I suppose it would've been the topic of some conversation since she her infamous role in the Battle of the Binary Stars). I got the impression that there might have been more than a platonic relationship there between them, and I hope they don't go that route. The more I think about it, I really wish that they had used Soval or T'Pol as her Vulcan foster parent to get away from any potential canon issues when it comes to Spock or Sarek. And watching the flashbacks with Amanda and young Michael, I don't get why Michael needed another mother figure in Georgiou. This would've worked better if Michael had little to no human companions or interaction while on Vulcan which prompted the foster parent to get help from Georgiou.
The most out of place character in this episode was Tilly. Her comic relief bits just didn't work for me. I hope they tamp it down in the future. I have no problem with her remaining socially awkward, but her behavior and dialogue often felt out of place to me in this episode.