Okay. First impressions.
A bit on where I'm coming from with this, for context: my favorite Trek series is TOS, by a long shot; second favorite is DS9. My favorite Trek film is Wrath of Khan. I absolutely loathe the first two Abramsverse films, although Beyond was at least watchable and felt passably Trek-like.
So. My first impressions of Discovery, after the two-part pilot? Like most posters here, I think it was a mixed bag. What interesting is exploring the reactions to what's in the bag and how it's mixed.
I think the writing was mostly good, although it clearly suffers from creative struggles at the top and from being written by committee. You can make a pretty good guess at which parts, creatively, came from Bryan Fuller and Nick Meyer (who are incredibly talented people), and which parts came from Alex Kurtzman and Akiva Goldsman (who are atrociously talentless hacks). As for current showrunners Berg and Harberts, I'm not really familiar with their past work (nor with how much creative control they're actually allowed to have here), so I can only wait for them to prove themselves.
As to what they all wrote: many parts worked. There were (a few) scenes with dialogue that seemed genuine and illuminated character, rather than just conveying exposition. Burnham's background seems genuinely intriguing, and the source of some interesting internal conflicts. I like Sarek's involvement. Saru is simply a great new character, with the potential to be a breakout favorite. I like the fact that Trek is finally getting a chance to do a long-form serialized story, rather than being saddled with an obvious status quo and a reset button. I've never been much of a fan of Klingon-heavy stories (I've never seen why viewers should be expected care about characters caught up in the travails of what is basically a premodern society, completely patriarchal, militaristic, and honor-bound despite its tech level, unless they're actively trying to change it)... but I do like the concept of positioning the Klingons as a fragmented empire attempting to reunite itself.
Some parts didn't work. First and foremost, most of the scenes of the Klingons talking amongst themselves could and should have been left on the cutting room floor. They undermined any sense of suspense and destroyed the show's pacing. What they were doing was interesting, but the way it was portrayed wasn't, and we should have discovered it piecemeal just as they crew of the Shinzou did. Meanwhile... Most of the supporting characters, from the admiral on down, were unfortunately written to be disposable and instantly forgettable. As in the Abrams films, the writers seem to have forgotten that space is Really Big, and give us absurdities like real-time communication across half a quadrant, or entire fleets of ships from scattered starting points converging to warp in simultaneously on a single point — things that may provide a brief moment of on-screen drama, but at the expense of logic and plausibility. And while I'm fine with the notion of Burnham becoming a Starfleet outcast and having to claw her way back to respectability (from herself and others), the way the writers got there was incredibly contrived... her mutiny was badly under-motivated, and the later decision to send the Captain and First Officer onto the disabled Klingon ship alone was sheer stupidity, on the level of the worst of past Trek tropes.
I didn't much like the visuals, and felt they were often at odds with the intent of the writers. People keep posting that they're "stunning" and "beautiful"; I just don't see it. Expensive, yes: you can tell they put a lot of money on-screen. But that doesn't make them interesting. The overall production design is far too evocative of the Abrams films, which is not a good thing. The ship designs are too cluttered and inelegant, and sometimes just baffling (why are cells in the brig so huge?). The uniforms are bland. The Klingon redesign is godawful (and as others have remarked, they missed the opportunity that was clearly there in the story, with the repeated references to "24 houses," to present a variety of Klingon looks). The needlessly quick cuts and ever-moving camera make it difficult to get a clear sense of where anyone or anything is spatially, especially during action scenes. This isn't helped by the lighting being far too low, which at best makes it literally difficult to see what's on screen in many scenes, and at worst actively changes the mood of what's being presented — as in the court marital scene at the end, where the inexplicably dark courtroom takes what would be a perfectly normal official proceeding and makes it feel like a hostile star chamber, very un-Federation-like.
The acting was a mixed bag as well. Michelle Yeoh is a talented performer, but she was given a ton of really wooden dialogue to deliver, and she delivered most of it woodenly.Michael Frain has a thankless task following in the footsteps of the inimitable Mark Lenard as Sarek, but he seems to be doing a good job of it so far. Martin-Green is a standout as Burnham, taking advantage of every little nuance of character she's been given, and making even plot-driven actions seem emotionally credible. The Klingons were a disaster; the actors should never have had to deliver all that dialogue in Klingonese, which clearly compounded the already tough challenge of acting through massive face prosthetics (and which kept the audience from noticing the visuals anyway as we were stuck focusing on the subtitles).
As for how the show comes across conceptually, as part of the larger Trek universe — including consistency with continuity, which, yes, does matter to me? I like that it's set contemporary with Pike and the original Enterprise, and I think there are awesome storytelling possibilities there with the potential to explore the background of the TOS era in a way the show itself seldom could. To me, that era has always been the true heart and soul of Trek, and putting it in another century would have far less resonance. I don't like that it doesn't look like it fits that era, but again, that's the production design in conflict with the writing. It's odd that the show would remember and refer to Donatu V, for instance, a nice callout to one line of dialogue from a single episode 50 years ago, yet change the Klingons in a way dramatically at odds with scores if not hundreds of previous on-screen hours... and it leaves me wondering who's really in charge of the show and making the final creative decisions about these things. Still, on the whole, it seems like the writers appreciate that details matter — even if they occasionally blow it, as, for instance, in a moment when Captain Georgiou calls across the bridge to "ops," a jarringly 24th-century term, rather than "helmsman."
On the whole, Discovery seems to have a lot of potential to be great — but also a lot of potential to go badly awry. I wonder now much influence the network has on the content; hopefully CBS's (hamfisted) attempts at marketing haven't led to undue creative interference. Obviously the network wants the show to help anchor its new streaming service, but that's a heavy weight to carry, and — at least right out of the gate — it's hard to say whether the show is up to it. Certainly it didn't wow me and grab my attention like the premiere episodes of some other SF shows, even with lower budgets (e.g., The Expanse or Dark Matter), never mind "prestige" series like Game of Thrones. If it weren't for my affection for Trek, I'm not sure how long I'd stick around. But that affection does exist, and I'm willing to give it the benefit of the doubt.
