I have seen all of SNW season 1, a few episodes from season 2; and none of seasons 3 and 4.
No spoilers, please.
I recently re-watched season 1. I think it's mostly very good. There are a few things I didn't enjoy.
1. I think Hemmer's death was pointless and unnecessary. The episode could have concluded with one less death without throwing off the narrative. Having a legally blind actor portray a blind, and amazingly capable, character. A well acted, and very interesting character. Awesome! Then, killing him off. What the hell.
2. In TOS the Gorn are introduced as being aggressive, and wearing fabulously sparkly outfits. Eventually, there was clarification that their nascent conflict with the Federation wasn't an invasion, but a misunderstanding. The Federation is not always good about checking if an area of space has been staked out by someone else before moving in. The Gorn were fighting off perceived invaders, not just being rampaging maniacs.
The SNW Gorn are, as La'an says, monsters. No subtlety. No redeeming qualities. Just hunting, killing, and/or laying eggs in anyone they come across. I'd think their intergalactic neighbors would have tired of it, and wiped out the Gorn by now. Hopefully writers dial back Gorn behavior in subsequent seasons.
3. TOS' Chapel dealt with a 1960s depiction of her continual, kind of desperate, a restraining order cannot be far off, romantic chasing of Spock. But, SNW's Chapel, wow! She is every good thing about TOS's Chapel, and so much more. Then, Chapel started mooning over Spock. I'm not digging this '60s throwback behavior.
4. Sam Kirk. I have nothing against the actor. I just wonder why the heck Sam Kirk is even on the show. If SNW had 22+ episodes per season, instead of 10, I'd still wonder why the heck Sam Kirk was on the show.