So much happened in "Penguin's Umbrella" that was built up by the all of the previous episodes that I'm just going to summarize where everyone is by the end of this episode.
Jim Gordon: Right after the Major Crimes team of Montoya and Allen arrested Gordon for the murder of Cobblepot, the man himself walks into the police department. The charges are dropped, but now Fish Mooney, her secret lover Nikolai, and their boss Falcone all want Gordon dead. Rather than run away, Gordon decides to tackle the problem head-on and arrest the corrupt mayor and Falcone. Ben McKenzie (Gordon) delivers his best line of the series so far when his captain asks if he's crazy, "No. Maybe a little. Feels good."
Gordon decided the best solution was to die trying to arrest Falcone, but he backs down when Falcone states that he has Barbara, Gordon's fiancée. And then, for no clear reason, Falcone lets Gordon, Bullock, and Barbara go. After the trauma of the events, Barbara and Gordon have an emotional reunion and now that the truth is out, Gordon won't be under the weight of MCU's investigation. He also has a new relationship with his partner.
Bullock: Initially furious that Gordon didn't kill Cobblepot (Donal Logue adds just enough fear to the character to make his threats against Gordon compelling), Bullock gets drunk and eventually decides to ally himself with the good guys. He figures he's a dead man either way, so he may as well join Gordon's side. It's a sudden switch for the character, and one I expect will remain permanent. While it should create some fun dynamics to see a dirty cop try to go straight while taking on the mob, I was hoping for more background on Bullock's past, which we likely won't get now.
Montoya and Allen: It's brief, but important. Through this entire series, Gordon and the MCU have wanted the same thing: to fix Gotham City. Now that the truth about Cobblepot's "murder" is out, they can finally start working together, so we'll see Gordon, Bullock, Montoya, and Allen working to stop the crime and corruption. It also looks like Captain Sarah Essen is starting to come around.
Cobblepot Penguin: It appears Cobblepot has fully accepted the moniker of Penguin. Really, this entire episode is about him. He's the catalyst for the change and he has some major moments in the episode. When he takes down one of Maroni's lieutenants, he does it because he knows that guy is cheap, and Penguin simply pays his henchmen more. Robin Lord Taylor has been great this season at appearing weak and scared but then revealing his control over a situation, and he does this repeatedly this episode. By the end, it's suddenly hard to tell just when Penguin hasn't been in control.