My first exposure to Star Trek was with TNG in its first run starting in 1987 and watched everything all the way to the end of Enterprise, and all the movies ending with Beyond. It's kind of weird to realize the difference in time between ENT and Picard is the same as between TOS and TNG.
I recently watched all of Discovery, thanks to signing up for PIC, and I have a mixed but generally positive opinion of DIS. I like that it is willing to try new things, and some of the the characters and plots are genuinely good, but it is severely hampered in a few ways.
I had to completely ignore external continuity to allow this show work for me. Trek has always suffered in the realm of continuity, which is why I am willing to actively ignore it, but it is particularly glaring in DIS. In other Treks the continuity errors can be reconciled with some ease, but not in DIS. It is actually a bit shocking, because it suffers poor internal continuity as well, which is weird for a show with a tight arc and which is likely intended more for binging rather than a serialized pace.
The weakest aspect of DIS is unfortunately the protagonist, Michael Burnham. Her being a godly figure is not really an issue, Kirk can be that way occasionally, but it doesn't help. The real issue is if she is present no one in the same scene can form a complete idea, act morally, make a decision on their own. If Michael Burnham says something has to be done a certain way it is almost certain it will be done that way before the episode is over. This kind of power over the plot and characterization of other characters should place her as captain, or at least the first officer, yet in the first season she is without rank, and in the second she is a commander but still not first officer. Thanks to her DIS wastes half its ensemble cast.
This inadvertently makes the best scenes the ones without Michael Burnham, because it allows the other characters to act and think on their own. But even then, it is not until season 2 that the show seems to realize there are people other than Michael Burnham, the captain, Saru, Tilly, Stamets, and Dr. Culber. Episode 1 of season 2 the two women at the front of the bridge seem to double their lines over those of the first season.
Lastly, it does not earn its emotional moments. When ever there is a scene where Michael Burnham is supposed to be sad about someone's death, or impending death, it is always unearned. The best examples are the first episode where Burnham mourns the loss of her captain, who we just met about an hour ago. We have no familiarity for the character so it falls flat. Same thing happens again when the cyborg woman dies, because in all of two seasons we never learned anything about her except at the last hour before her death. It happens again when Saru calls Burnham his best friend even though he had repeatedly called her a dangerous predator, and again in the second season episode 12 where the entire episode is people writing loved ones we have never seen.
So what are the highlights? Stamets and Culber are not only individually good characters with well handled arcs, they are good characters as a couple. I think they epitomize the show-it-as-unremarkable ethos of TOS in how their relationship is handled. I got really involved in their story, far more than anyone else's and would have been happy to have more focus on those two, which is part of why I'm pleased with season 2.
Saru is an interesting character, with a significant and fairly well handled change to his characterization in season 2. He also comes from an interesting personal background, and his species as a whole has a history which I would call very Star Trek.
Tilly is not my favorite, she is kind of a Wesley Crusher, except I like Wesley Crusher. The twist is, by the end of the first season she mellows out as part of her arc, and gets some confidence, which combined make her rather likeable. But she becomes annoying again in new ways in season 2 which kind of ruins her progress from season 1. I like her more than I dislike her, in part because she is allowed to do interesting things away from Burnham, and she has built up a believable relationship with Stamets.
Jet Reno, an engineer they pick up in the first episode of season 2 is criminally underused given how she dominates in her scenes. She shows up maybe 3 times in 13 episodes, and is critical to the final episode. Hopefully she is used better in season 3.
Last but not least is Vice Admiral Cornwell. Something about her is spot on as an admiral. I don't know what it is, but she really works well in her role, and I wish the material she had to work with was a little better.
Spock is a huge highlight. I was worried for his character, and while he does have one idiotic line, "I like Science," for the most part he is in character and the only one able to hold onto his personality in the presence of Burnham. He's seriously great, and Baby Spock is too cute.
So there were complaints about the show being this and that, and I half expected to see gay sex on the bridge, and men being cut off mid-line all the time. None of that panned out, but the second season just about bends over backwards to put women forward, and the only straight white men with real presence either get unintentionally undermined as characters (Pike, who is at least bookended perfectly by his TOS story), or are villains (the two Section 31 men). Also the douchbag scientist who dies by asteroid because he disagreed with Burnham in episode 1 of season 2. Fortunately this is fairly minor, even if it is really obvious.