Discovery is a totally awesome series.
I've watched all the previous 6 Trek series numerous times, likewise all the movies, read every single novel, almost every non-fiction book about Trek, gone to many conventions, met many of the actors (including a private lunch with Majel Barrett), and so on. I'm not saying this to boast or brag, but to illustrate that I've immersed myself with Star Trek for most of my 55 years of life. I love Star Trek! I love SF and have read widely and watched practically every SF TV series ever made.
Discovery isn't set in the previously known Trek universes. That is why the Klingons are different, why the technology and people are the same in some ways, yet different. Thus, these aren't inconsistencies with previous Trek, but a wondrous new canvas to creatively draw upon. The mirror universe concept is ripe to explore and Discovery has done it superbly.
It reminds me of the Battlestar Galectica reboot... similar yet so incredibly modernized and expanded.