Pro: Spoiler Enterprise redesign looks great. Not too much like the original design for it to look outdated, yet not too dissimilar for me to buy that it's the same ship. Con: Glaring scientific visual mistake in episode 4 - an O-type star that looks like a m-type "red dwarf" to me. (O-Types should be blue-white supergiants).
Pro: Its the first new star trek series in over a decade. Con: there hasnt been a likeable character yet in the whole of season one.
Pro: Amazing cast and characters that make you care about them. Con: Episode length. I'm fine with 13-15 episodes. What I don't like is that they touted that since they're on CBS All Access, they're not bound by the time limits of normal television, which have to account for ads. That made it sounds like we might get some longer episodes. However, we still got our regular 45ish minute episodes and one that was really, really short. I'm not saying make them feature length, but take a little more time (where it counts) to make sure the stories are done justice!
Pros: The serialized storytelling. It allows for in-depth storytelling and world building. It brings Star Trek to the modern world and presents it in a contemporary way. Probably the best possible approach for Star Trek in 2017-2018. Cons: The serialized storytelling. The older I get, the harder it is for me to pay attention to things, especially long, serialized TV arcs. Sometimes I miss classic story-of-the-week Star Trek. If you could gave me 13 'new' episodes of TNG, I'd be squeeing louder than you could imagine.
(This pertains to season 1.) Pro: Great attention to details on the props and a wonderful update to TOS designs. Con: I guess nobody got the memo about the uniforms.
Pro: Many likeable characters imo. That includes Burnham, aside from those early bad decisions, that I still struggle believe she'd actually make. Con: Most of the lengthy monologue speeches. They seem to be there to remind us that this is still the Federation and Starfleet that we know and love, but they feel a little too overdone.