Personally, I'm ignoring the concept that this is tied-in with any of the other ST series. That means I can ignore the timeline plot holes, the stupidity of the Klingons, etc
I loathe the central character, especially the way she's written and the way she acts - I really found it jarring when she gets the Will from her former captain, hides it away (emotional moment) then gets a call to the bridge and literally swaggers out of the room and the seems to take a gentle stroll through the ship - not in any hurry to report to the bridge where she's obviously been summoned by the Captain!).
The Klingons are dreadful. Obviously they're going for a religious zealotry angle to tie in with modern times but they're just so poorly written. As someone suggested earlier, it seems obvious that the actors have real issues speaking with those ridiculous teeth (which, incidentally, totally look glued on to their normal teeth - it's like something from an AmDram production) whilst I think is why they speak in "Klingon".
However, in the defence of the show, I think a lot of the criticism aimed at the Klingons is flawed. Everyone is saying that they don't act like the Klingons from TNG, DS9 and STV but all of those should be discounted because this is supposedly earlier in the timeline or in a frankly different universe (IMO). It's like everyone saying that Superman in "Man of Steel" isn't like the Superman they all know from Reeves films, Smallville or Lois and Clark, despite the fact that its supposed to be a separate timeline/reboot.
Having said that, the only characters I like are the First Officer and Lorca. I'd happily watch the rest get spaced.