Batwoman 0 is a nice overview to bring in new readers, and the cover is awesome. But much as Batman's narration as he observes Kate works as an introduction to the character and as much as it's in character for him to observe and judge (see the Batman Returns One-Shots!), I wish they'd just told this as a Batman-free story. Yes, she's got the Bat on her chest and in her name, so of course, Bruce would want to check up on her, but it takes the focus off Kate a lot and this should be her book and the focus should be on her for a while. Bruce would've been more welcome by me coming in later in the series.
Zatanna comes across as somewhere between pure fun (a la the first 12 issues of Power Girl) and the more serious books (Green Arrow, Green Lantern, Batman, Batman and Robin, etc.) The tone so far is probably closest, of those I read, to Gotham City Sirens. I enjoyed her cousin Zach's appearance, and the magic is playful with some edginess, and so far, nothing Earth-threatening. In fact, it's been on a mostly personal level. As for the art, I normally don't like so many artist changes so early in the book, but when the artists are as good as this group, I don't mind so much. Roux's issues were nice, if Zee sometimes looked a bit young. Hardin's pencils were fine if average. Saiz did a nice job with Zee, and Cliff Chiang's issue (8) is my favorite, so far. I am looking forward to Jamal Igle's work on the book, starting with issue 11. This isn't a must-read book for me, but it's a fun one to spend time with. With my disappointment in and dropping of Power Girl, it's nice to have another female character step in to entertain me.