Barbara Kean has been a weak link in Gotham since day one. Coming off as unlikeable from the very start, it was a relief to see her relationship with Jim come to an end. It's hard to say whether they want us to hate her or if those working on the show just aren't sure how to write a female character who isn't Fish Mooney or Selina Kyle (and neither of them had the best arcs in Season One), but that short-lived and randomly thrown aside lesbian subplot shows that they were never quite sure how best to handle the character. Oddly enough, things started looking up when she was kidnapped by The Ogre, but even that took a bizarre turn thanks to a last minute reveal which saw Barbara announce that she had murdered her parents. She then tried to kill Leslie Thompkins, and her fate was left unresolved. Presumably she'll end up in Arkham Asylum, but the character has been so poorly handled up to this point that it's near impossible to imagine how she and Jim are going to end up reigniting their uninteresting romantic relationship somewhere down the line. Unless Gotham is going to bring back Barbara (who has suffered from some mental issues in the comic books as well) as an almost entirely different character, it's hard to imagine how she can be redeemed and made an interesting part of this series. Her randomly shacking up with a couple of street kids - Selina and Ivy - who had broken into her apartment was weird enough, and yet another example of Gotham throwing shit at the wall to see what would stick. In Barbara's case, nothing has so far. If they can't fix her at this point, ditching her from Season Two fairly early on would be no bad thing.