Batwoman’s sixth episode has several surprises where they diverge sharply from most other versions of Gotham City. There are also a few things that touch on some of the movies and even the recent “Gotham” tv series.
I have to give the writers on Batwoman credit for diverging some from the pattern of the other hero shows they’ve done on the CW. They set up the status quo, but didn’t immediately drop into “villain of the week” mode. The background issues are still around, and arguably more important than this week’s villain.
The pilot episode established the basics of what we needed to know about Batwoman, introducing the various characters, some back story, and at least the broad outlines of the status quo.