Series It's bad.
When the first trailers dropped for Batwoman, the whole thing looked like a challenge to those sexist internet geeks who spend countless hours complaining about Mary Sues and "SJ Ws" in their franchises. Batwoman, aka Kate Kane, strides in as a cock-sure, progressive, hero protagonist who apparently communicates only in girl power slogans. And whilst those geeks deserve a good winding up, I liked the idea of an outspokenly feminist DC superhero show, at least to make up for Supergirl's tame and unconvincing attempts to address superhero sexism.
I've not read a Batwoman comic. If this show is an accurate representation, then they must be pretty boring. Kane, Bruce Wayne's niece, grew up hating Batman because he once failed to save his sister and mother from a deadly car accident. But with Batman having disappeared from Gotham, and a new Alice in Wonderland themed villain attacking the city, it falls to Kane to stop her. Kane discovers Batman's costume, forgets her grievances against the Bat, and decides to adopt the mantel for the purposes of taking down the mysterious enemy.
There are a lot of sloppy and unimaginative creative decisions that stick out to me: Kane's narration provides a constant stream of cliches and mixed metaphors ("Wayne Tower is the beating heart of the city, with eyes everywhere"); Her Batwoman costume is badly designed and gives her a stupid lollypop head; Alice, the villain, is just another crazy person with a boring literary theme and massive daddy issues; At one point in the pilot, we see Kane enter a deserted Orphanage, which instantly transforms between shots into an industrial warehouse corridor. It's a pack of bad ideas and clumsy execution.
I mentioned a villain with daddy issues, Kane also is also largely defined by her poor relationship with her father. Kane's dad runs CROW, an elite and brutal private security force. It seems weird that Kane - an outspoken rule breaker and anti-authoritarian - would not only buy into Batman's violent authoritarian tactics, but also keep siding with her dad's murderous cops. It's only because Kane suspects Alice might be her long lost sister and might get killed by CROW that she shows any reluctance for this working relationship. She shows no pity for the incapacitated henchmen CROW kill, and in the context of a modern audience sitting through ongoing Black Lives Matter protests, it comes across as especially thoughtless.
So what I'm basically saying is that Kane is a selfish asshole, and I'm not clear if this is a bungled attempt at making an antihero, or simply an accident of bad writing. Despite the trailer suggesting she is a cock-sure girl power figure, Kane spends an inordinate amount of time negatively comparing herself to Batman. Many in this show's audience will be doing the same.
Series Strong first season, despite being cut short
As a massive Batwoman fan prior to this show, I quite enjoyed the first season and found it, on the whole, to be a sensible adaptation of the source not only into a different medium, but into an existing universe.
I especially appreciated the changes made to Kate, because they felt deliberate and informed by the rest of the world rather than changes made for their own sake. This Kate, for instance, didn't emulate her father in the aftermath of their family tragedy like her comic counterpart did, and thus the two end up in different places.
I have little to complain about in terms of the acting or writing. The main cast all played their parts well, and their characters all got at least a decent amount of development and storylines. Mary seems a bit underdeveloped on that front, however, though she's an enjoyable character. Otherwise, it was fun to see all that character stuff weave together as the season went on, particularly in the later half with Luke's story.
More generally, the season-long story and the smaller episodic stories were all interesting in their own way, with no major structural issues I could see, and I very much liked how several one-off episodes ended up being major pieces of the whole. Again, most of the strongest episodes this season are in the second half.
The cliffhanger was a very fortuitous cutoff point for the shortened season for how massive it was. But how that will continue on after Ruby Rose's depature is up in the air, now that season 2 will also be tasked with introducing a new lead. I don't know how it'll be done, and I have my own reservations about a new lead... but after this season, I have confidence in how it'll go.