First of all the good; the show , imo, looks great - the sets and special effects are top notch. Umm , I cant think of anything else ...
The weaknesses all stem from the writing. Historically, as best as I can recall , you would get a Star Trek series that, if it had 20 episodes , would offer up 21-22 stories ; one or two stories that lasted a season but otherwise one story per episode . Not so in this case, essentially you have one story told over 15 episodes, if I was quicker on the uptake I would have taken that as my first indication that the writing was going to be weak - that was only confirmed by the sudden switch over into the 'alternate universe' trope a desperate writing move that most programs don't reach until they are midway through season 4 or something not halfway through season 1. None of the main characters are particularly engaging , not as appallingly misjudged as some of the characters in Star Wars (Ep 1,2,3) that come to mind but that is hardly a complement. If you are a fan of the genre and a bit of a completest then watch the series and come to your own conclusion but unless they put some serious effort into improving the writing I won't be coming back for seconds.
I have always been a Star Trek fan and enjoyed the various versions of it over a long period of time. This particular series seems a little disappointing. There is plenty of action, rather too much for my liking. A little frantic. The humour and subtlety of earlier series is lacking. And the Klingons look like bank robbers in masks. They have completely lost their horrible appeal from before. Oh well, perhaps I will get used it. I have seen only 2 episodes so far.
Star Trek has its own style, its an optimistic view of the future. The problem here is that the writers don't seem to grasp that and instead its just another sci-fi show dressed up as Star Trek. Most of the problems with this series come from the weak writing which I guess isn't too surprising because you'll notice a lot of the same people involved with this are also involved with the weak alternative universe films.
Overall its a missed opportunity. Michelle Yeoh made an awesome captain in her too brief appearance. A series where she had been the captain with a better group of writers would have been outstanding.