"Discovery" got a notoriously awful start: the first episode is appallingly bad, and most reviewers - unsurprisingly - went live with terrible reviews based on that episode. The second episode is merely bad. After that, things got more interesting: it's good to see Star Trek taking chances, doing different things. It's also good to see them telling a larger story arc with the expectation you should watch the episodes in sequence and remember what's happened (although they bracket all the episodes with "previously on" and "coming up on" blocks, each a couple minutes). The down-side of this more chronological story-telling is that they're perfectly happy to use it to make cliff-hangers at the ends of episodes. I am NOT a fan of cliff-hangers: they're insulting to the fans. You don't think we'll come back unless you leave the fate of your characters in doubt? You don't think much of your own product then, because we'd be coming back if it was any good ... Another mixed blessing here is that they're clearly willing to kill off major characters (this is a war, after all) - which means that, unlike other Star Trek series, a cliff-hanger actually carries weight.
SPOILERS FOLLOW - stop reading now if that matters to you.
The first major problem I have with the series is they've changed the appearance of the Klingons AGAIN. Unnecessary and pointless. The first couple episodes rushed through the start of the human war with the Klingons - and simultaneously set up Michael Burnham as a mutineer (with the best of intentions). If they'd taken more time, two or three more episodes to set up the politics and characters, it could have worked better. But they were in a big rush to get to the big set pieces of the episodes coming up.
Which includes the instantaneous-go-anywhere spore drive (because no one has ever taken a trip on mushrooms before). Not to mention that this doesn't fit anywhere in Star Trek's overall mythology. And a character who appears Human but is in fact Klingon ... I can accept Cylons who look human, sometimes don't even know they're not human. But a Klingon so modified that they can pass for not only human biology but also human psychology? I'm not buying it as described. And then we get into the alternate universe AND time travel thing: they use both in one fell swoop here, avoiding any need for consistent plotting by resurrecting characters across time-lines.
I left after the 13th episode, when after about four episodes spent in an alternate universe (full of evil humans - we can track that concept back to the original series, hardly a new idea - but they came back nine months late to a war with the Klingons almost entirely lost. Which leaves them with two plotting options that I can see: time travel again (but they're out of mushrooms) or stay in the current time and save the day with their Klingon invisibility cloak breaker. Either way, they need more mushrooms, and I feel pretty sure that I'm not going to like the magical methods by which they get them - too many gods in the machine.
I have mixed feelings about the show. They're taking chances, which is a necessity when the series is over fifty years old: you HAVE to break new ground or you're just going to do the same old stuff. But they're doing it with magic technology: not small increases in tech as always happen, but huge leaps and bounds that have no place in the Star Trek cannon. (I'm not a Trek purist, but I strongly prefer universes to be internally consistent.)