I'm a big Trek fan and I enjoyed it a lot, I do admit I found the artisic style quite jaring and it's gonna take some getting used to though.
As far as the Klingons go I don't mind it, I would like it explained though at some point even if it's just a nod. Burnham and Saru added quite a bit of personality and those 2 look like they're gonna be the anchors for the season which I look forward to. As for the adversary, T Kumva isn't it ?, I reckon the show is going to put Kol as the identifiable Klingon and he looks slightly more 'traditional' look than the others - Leather outfit n stuff, I hope they can give him a heart rather than a cardboard cut out villain.
I also liked the whimsy fun, although a bit lacking but it is a prologue and I hope they add more to it, when they both retreated to the Captains room to look through the telscope I grinned and never stopped til the end of the 1st ep. Also hoping they have some eps where they give the audience room to breathe, some good old character building, stranded on a planet or sommat made the older shows what they were. I also hope they respect canon, I know they've already got loose with it with the Klingon cloaks and that is something I can see that will eventually annoy me, don't mind a few minor mistakes but if it becomes commonplace I'm gonna start whinging.
All in all it's still early days but it's got off to a good start for me and this is an achievement in itself because the last thing I wanted was CBS to be proven correct and have them declare ST dead. 10 millions views for the broadcast, most watched non sports event for the day and CBS all access breaking sign up records.