Why are you not happy about Pike in it, Kat?
I don't really have the need for nostalgia throw-ins that they seem to think are necessary to get people to watch a prequel Trek show. I'm not particularly interested in Pike, Spock, Sarek, etc. showing up, though it doesn't horribly bother me either. Mudd is a bit more fun but them trying to shove the classic Trek stuff into the show at random intervals I find contributes to the overall uneveness of the show. (Though they have new show runners and such this season 2 so there may be less uneveness going forward -- we're kind of behind watching at my house as we've been playing catch-up with multiple shows.) I also think that it is 2019 and we don't need Discovery to have another noble jawed white guy captain again. They could have just kept Saru captain. (Of course Saru mutinied at one point, but in this show this is apparently not an issue.)
As someone said, the Klingon speech is a bit annoying. I don't know why they made them look so different.
There are rights issues between Universal and CBS regarding design trademarks that require various details to look at least partly different from previous versions. The Klingons were already something of a mess, since their appearance radically changed between Classic Trek and TNG decades later, but an explanation was made for this in the larger Trek canon as experimentation that the Klingons did as a disguise, an idea that Discovery then borrowed for its show. Plus show special effects people tend to like to play around with the designs. In Discovery, they tried to come up with a design that was in the neighborhood of the TNG onward Klingons but different.
However, that new design was not well received. Since Klingons are often identified symbolically with black people, with a number of prominent black actors playing some Klingon roles such as Worf, that the Klingons now looked more monstrous and acted more brutishly and serpent-like, as well as the idea that an albino was an outcast for his color among dark skinned Klingons -- that all didn't play well with a lot of people. Others thought that the Klingons were being made to represent Trump supporters and making them look monstrous, etc. And for some reason, the Klingons spoke Klingon really, really slowly, even though they were using subtitles. So in Season 2 of Discovery, the Klingons are further revamped, with the idea that different houses of Klingons have somewhat different appearances. So it's still a mess.
They also should be using the classic uniforms. I could accept Discovery having different uniforms for some reason, but why would the officer at the penal colony have their uniform? Everyone everywhere in the Federation that Kirk talked to always had the classic uniform. It doesn't make sense!
Again, there were trademark issues on having the exact same look, plus the mini-skirts on the Classic Trek uniforms for women were problematic in the current era. Discovery takes place at least a decade before the Classic Trek era, so the idea they came up with was that the Enterprise, a new important ship, was sent out on a long range exploratory mission before the war with the Klingons began and they had the
new uniforms upon their launch -- which are the Classic Trek color coded uniforms with some modifications. The Enterprise was ordered to stay away and maintain communications silence during the war. With the Federation being at war, they did not have time to give everyone else the new uniforms like on the Enterprise and stayed in the old ones, as did the crew of the Discovery, which was a new, secret ship until taking lead point in the war, and as such the Discovery crew was not issued the new uniforms either. With the war ended, eventually everyone will get the new uniforms, which are the modified version of the Classic Trek uniforms, but that hasn't happened yet.
That allowed them to make some jokes on the show about the "new" uniforms that the Enterprise has that no one else has yet. And it also provides issues for the two crews -- the Enterprise crew feels guilty and unhappy that they sat out the war and were cut off. The Discovery crew is envious and a bit disdainful of the Enterprise's shiny newness and lack of trauma. So I thought that one worked okay, as militaries do frequently revamp their uniforms. Otherwise, Discovery as a show often doesn't really properly match the timeline it's being a prequel of. I personally just view Discovery as happening in another alternate timeline, like the current Trek movies -- similar events but things are somewhat different. In Discovery's alternate timeline, Spock did not have a brother and had a human foster sister, etc. And the Klingons evolved to look different than in the original Trek timeline. Given all the Mirror universe stuff on the show, it seems appropriate.
Overall, Discovery is okay, finding its sea legs like all the Trek shows. But I'd really love some new Trek shows that use the world of Trek consistently, but aren't draped in nostalgia of the past shows. I have less interest in prequels than moving forward. I thought the idea of a Star Fleet Academy show had some promise and they are apparently still developing one. I love Patrick Stewart but I'm not really interested in an old man Picard show. And Michelle Yeoh was/is terrific, but I can't get that excited for another prequel show about her character either.