Unfortunately I only got to see parts of the pilot they showed on CBS. From what I saw I thought it was a mixed bag. It looked great, Sonequa Martin-Green was fine (both in looks and acting) but overall the writing and characterization felt choppy and shaky. I felt that CBS wanted to ramp up the action, drama, and emotionalism at the expense of organic character building.
Still not a fan of James Frain as Sarek. While I think Michelle Yeoh was good casting, her line delivery was too stilted for me and there was a distance too often between her and Martin-Green for me to fully believe they had a mother-daughter/mentor-student kind of relationship. Burnham also came across as too trigger happy, but once again, I think that was done for the sake of increasing the action and drama. I liked Doug Jones as Saru. I liked that how he was into self-preservation, that isn't a perspective you see much of in a Starfleet officer.
As for the Klingons, the production design was on point. I'm still not a fan of the redesigned look for the Klingons but the production values were good.
I also had some issues with the continuity gaffes or overturning. I noticed that the 100 year absence spoken of in the pilot conflicts with what Spock said about the 70s years of hostilities between the Federation and Klingons in Star Trek 6, which would have put the start of that conflict in the 2220s. But Discovery now has it that the Klingons pulled back from interacting with the Klingons in the 2150s. Perhaps it was related to the Earth-Romulan War. I do hope we get some answers about why the Klingons pulled back.
Other reviewers have pointed out the hologram communication technology. Really, the Sarek hologram was more advanced than what we saw in the 24th century with the exception of The Doctor. I also feel overall that the ships and other tech looked too advanced for the time period.
I don't get why they just didn't put Discovery in the 25th century. So far, nothing I've seen demands that the show predates Kirk's Enterprise. Granted they couldn't use Sarek, but Tuvok could easily have filled that role.