I have a few conflicting thoughts and feelings on Disco, as I've seen it called, so I'll try to lay those out in some more-or-less coherent form. But that'll be difficult, because just like my feelings about the show, Disco itself is a bit all over the place.
Let's start with a positive, though. The show looks great. There's clearly been a lot of time and money spent making the sets and uniforms and effects look not only good, but also distinctive. This doesn't look like JJ-verse Trek, which is neither a good thing nor bad, as the reboot movies have always looked amazing. It's done a good job of setting itself apart, visually, from everything that came before, while also looking appropriate to what you'd expect.
The uniforms are well-done, looking like they belong in the same universe as other Starfleet uniforms, and the ship looks like a Starfleet ship. The effects are also subtle, avoiding the early-CGI cheapness we got with Voyager (to take an example at complete random). For example, the tardigrade of the early parts of the series looks like it's actually in the room with the actors - even recent shows like the CW's Flash sometimes look like they've lifted footage from video games.
Plot-wise things are a bit more of a mixed bag. An uncharitable part of me wants to quote an old joke my dad always tells, that "there are good things and new things here, but the good things aren't always new and the new things aren't always good". But I think it's more complicated than that.
Instead, I'd like to quote the AV Club's definition of fan-fiction, from a recap of episode 13:
It’s a show that uses the tropes of an established franchise without any real understanding of how those tropes work; and it’s written without the craft or patience necessary to tell a story that means something outside of our recognition of those tropes.I hadn't even finished watching the show when I first read that, but it sums up perfectly my thoughts on what they've done with it. Although even that feels a little harsh, given that I liked a lot of stuff about it.
The overall story, of the first war between the Klingons and the Federation, is told well, and resolved in a manner that fits with the vision of Star Trek. It's too bad that the Klingon messiah, T'Kuvma, is eliminated in the first episode, and that his second-in-command, Voq, also disappears early on, to be revealed as Lt. Ash Tyler.
But the plot about Tyler being a vessel for Voq to infiltrate his enemies and sow chaos is a neat idea, though like many things on Disco, it's not clear where it should lead. There's no indication that he's waiting for a time to kill Michael Burnham or Captain Lorca, and he doesn't transmit details of Discovery's spore drive to the Klingons. There are reasons why, as he's ostracized and exiled from the Klingons, but the sense is that he's inserted himself into Tyler's psyche so that the show can have that reveal and also Burnham's conflicted feelings about having bonked a secret Klingon.
Lorca's also an interesting character, though again, I'm not sure how well his plot line holds up. The questions of how trustworthy he was as a captain were well-handled at the start, but once he's revealed as the Mirror Universe version of himself he just becomes an asshole. I'd have liked to see more fallout from Starfleet (especially the admiral he bonked, as there's clearly a lot of bonking on this show) on the fact that they didn't detect him for so long.
Burnham has a good arc, overall, but in those first two episodes I actually found her to be even more annoying a character than Neelix, from Voyager (who's just awful and such a drag on what that show could have been). She gets better, although in the end I'm not sure how earned her progression is - remember that it took the Next Generation seven seasons to show us how much Captain Picard had changed.
The one character I'd hold up as being really well done is Cadet Tilly. She's introduced as the kind of scatter-brained younger woman that seems to be in vogue in entertainment these days (Exhibit A is Felicity Smoak on Arrow), but the writers gave her a lot to do, starting with assisting with the spore drive. By letting her get good at something, the show also let her become the conscience of the show, espousing the values that Star Trek represents when other characters are toying with ignoring them.
The rest of the cast ranges from underdeveloped to "meh". It's a shame to relegate Doug Jones as Saru here, because I like him as an actor, but I hold out hope that as the show continues it'll develop him further.
Back to the fan-fiction stuff: though it was kind of neat to see Rainn Wilson as Harry Mudd, in the context of the overall story it didn't add much. And the spore drive thing was a neat way to move the plot along, but even in the first half of the season, it felt inconsequential, given that we know Starfleet doesn't use spore drives in the later/earlier shows (this reboot business is confusing).
I'd also like to single out how stupid killing off Commander Landry in the early episodes was. Not that I had any real interest in the character, since she was underdeveloped to begin with, but opening the tardigrade's cage and standing in front of it has to be one of the most pointless deaths in the history of television. They clearly had to get the security chief role open for Tyler, but it would have been good if they could have found some way to do it that was more organic. Also because the reveal of her character in the Mirror Universe fell a bit flat - she was so underdeveloped to begin with that it's not much of a shock. She's an asshole in the regular universe, and she's a follower of Lorca in the Mirror Universe (so, an asshole). Big whoop.
The tardigrade storyline was also disappointing, and a case of the "good/new" dichotomy. You don't have to be ridiculously well-versed in Star Trek to have seen immediately that the poor tardigrade was misunderstood, and that by using it to power the spore drive Starfleet was enslaving it. This is a trope that's been explored before, multiple times, and almost always to better effect (see: Devil in the Dark). The time resetting plot that marked Harry Mudd's second appearance was also kind of blah, as again, other Trek has done it better.
As for the structure, I'm ambivalent about the switch to serialized storytelling. It seems to have become the default way of doing TV, without regard to whether it suits the story being told. And while the old model, in which shows could be aired out of order for syndication, was a little cynical from a money perspective, there are pleasures to dipping into an episode at random sometimes and enjoying a complete story, with at least some closure. And more to the point, Trek has balanced standalone stories with serialized stories before, with Deep Space 9's Dominion War plot. It's one wish I won't get, but it'd be nice for season 2 of Disco to build its overarching storyline through multiple shorter episodes, so that the rest of the cast can develop.
When this show first came out, but before I saw it, I saw a number of folks online calling it the best Trek, or saying it stood up with the best. I can't agree. In terms of story quality, it's behind DS9, TNG and TOS, in that order; in terms of how Star Trek it is, it's also fourth, behind TOS, TNG and DS9. The storytelling wasn't as sophisticated as the very best Trek (and wasn't helped by randomly throwing in swear words, which I guess was to show how cool and with it this new Trek is), and as I said, the plots didn't always bear close scrutiny.
But... I didn't give up on it midway through. There was a lot to like, and it was interesting to see how the crew would react to a given set of circumstances. The other thing Disco has going for it is that Trek shows usually don't pick up until the second or third season, so as the writers better understand how the universe they're playing in works, I'll expect the show to get better too. And I have to give it credit for looking at the philosophical questions, which Voyager and Enterprise didn't always do well.
So it's not a perfect show, but I'll be looking forward to next season. I might even pay for CBS All Access, to watch it in the US.