Only a few things, since this is Star Trek and I'll watch it pretty much no matter what.
* Excessive violence. For me, Star Trek is escapism and it helps me feel more optimistic about the future of humanity. I don't have a strong stomach for violence, and I especially don't want to see it in the Federation utopia.
* Excessive politicization, if it's not done well. I'm okay with there being a political message, but it needs to be subtle. If they go way overboard and hit us over the head with Marxist ideas in every episode, I'll be out. But it would have to be pretty bad for me to give up because of this.
* Not having the "Star Trek" tone. If it just doesn't "feel" like Star Trek to me, I'll probably not be interested. I'm not really sure how to define what I mean by "feeling like Star Trek," but I'll know it when I see it.
Other than that, I'll probably watch it even if it's corny and full of technobabble. I can still enjoy that.