It's been pretty solid on that front. The lore it has been using has been on target if one looks at the totality of the canon.
Stuff like Picard's thoughts on Children and friendship with Data got talked about a number of posts just before this. Other stuff like the capitalistic nature of individuals and the overall stance towards Romulans from various people is very consistent with what came before.
If there's anything wrong with the show, it's that it totally misses the tone and style of TV Trek. The show being written like any generic modern sci-fi and the use of some silly new ideas definitely does not help but the basis seems solid.
For example, the warrior nuns are mad stupid but the idea that they have a rule that requires them to be upfront about their emotions is interesting. Romulans are portrayed as generally deceptive and more emotional relative to their Vulcan cousins so that rule jives well as a way of showing how different that niche of people are compared to the Romulan population.
I haven't really seen many things that are grievously wrong. There's been a lot of stuff that i don't agree with, particularly the direction they're taking, but they've been pretty mindful of Trek as a whole rather than one point in time.
They still forgot Lore exists and Lal.