I watched the 1st episode, I enjoyed it for the most part. I'm trying not to dissect it too much, though I had a couple qualms.
I realized that every iteration of Trek, from TOS to now, can be overanalyzed and nit-picked, so I'm trying not to let some of those things detract from my viewing. I tried giving ST: Picard more leeway as it went on, though I think it had more problems than just nit-picks (but I'll leave that for the Picard thread). But I'll mention a few thoughts I had.
Someone mentioned they thought it was unrealistic to have reverse engineered warp tech by "looking through telescopes" or something to that effect. While I'm no astrophysicist, I do know our space telescopes, and presumably the telescopes Pike referred to, are radio telescopes. They're not just magnifying telescopes. Radio telescopes pick up all sorts of information about cosmic bodies, so it's not impossible for me to think that a lot of information about how warp bubbles are created could be found from radio telescopic data.
I know this might be considered a nitpick, but I feel it's more than that: I didn't understand why Nurse Chapel was chasing the guy they were trying to sedate through the ship. Security should've been contacted, and actually should've been either in sick bay or guarding the doors. This is the kind of stuff that I feel is "lazy writing," where writers ignore what should happen in a situation just so they can have something happen in the story.
I also don't care for Nurse Chapel's character so far. Seems too different from the character we saw on TOS, and also seems a bit too contrary and flippant for a Starfleet medical officer. I thought the other characters seemed fine so far. The trailer made me worry about too much present-day lingo and attitudes being forced into the show. I'm fine with the show being a reflection of our times, but I don't want it to feel forced, or feel like the characters are just exaggerated caricatures. It's still too early to tell which way they'll go, though.
I had to look up Sam Kirk, since I wasn't sure who the character was supposed to be. I was ready to be upset over another "Easter egg" without substance being forced in, and it still borders on that, but at least his appearance doesn't seem to violate Trek canon, even if it feels a bit forced.
I'll leave you with this screenshot of Sam Kirk's only onscreen appearance, dead, played by William Shatner in a fake mustache:
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