I know this is an unpopular opinion, but I like the new show. It's a thinking man's show. It at times explores issues relevant to us today from an alien perspective but we darn well know it's talking about us. This is what the original show liked to do, for example all those times they found an Earth-replica planet but something on it had gone wrong in its past ("Miri" and "The Omega Glory"). Does it make much sense or is it realistic? Heck no. People should scoff at the idea of finding TWO Earth-replicas in deep space in the same series, if they have any horse sense at all. But once you accept that Trek is art and it at times tries to do some social exploring via this medium and in this fashion, you can just sit back and enjoy the show. Expecting it to be correct in continuity for every piece of hardware or weapon or gadget that they show is having the wrong expectations for this show, in my opinion, and frankly is saying that the show should have lower standards because it's basically a demand to sacrifice creativity for having the correct props or some stage-related issue like that.
I especially like how they succeeded in incorporating an overarching time-travelling paradox into the underlying fabric of the series, that's something that has not been tried before.