(There are spoilers here. Also, I ramble.)

I called Berg-Katze a magnificent villain who had been one step ahead of everyone all the time, so let me explain that. Berg-Katze said two significant things during its conversations: that humans would destroy themselves (in a big conflagration) and that what it was looking for was a suitable source of lots of fuel for this blaze. Berg-Katze's plan all along was to engineer this.

First, BK got Rui to create GALAX and empower the Hundred. This created something that BK could take over by impersonating Rui and a source of disgruntled ex-Crowds users, which BK then recycled into the Neo-Hundred to cause chaos. This chaos, concentrated into one place by the chase for the Prime Minister, created a bunch of paniced people. BK then hijacked the Prime Minister's broadcast and goaded all of these paniced people into becoming Crowds themselves. Berg-Katze's expected result from this was increasingly violent chaos as a whole bunch of uncoordinated people with newly-given powers stampeded back and forth, inevitably made mistakes about who was a 'bad Crowds' (and defended themselves from attacks by what they thought were bad Crowds), and so on.

(Psycho-Pass did a very similar take on the panic of crowds towards the climax of the show.)

At every step of this, Berg-Katze manipulated everyone to create the conditions for its next step. Nowhere was this clearer than when people restored trust in GALAX and distributed smartphones to everyone during the disaster to restore order, only to have Berg-Katze use this to reach everyone with its corruption of the Prime Minister's message and offer them the Crowds power. This wasn't an accident; Berg-Katze planned for this response to the Neo-Hundred. In fact the entire purpose of the Neo-Hundred and their chaos was to set up this situation.

Since I've seen some confusion about this: Berg-Katze didn't take over the Prime Minister's body during the broadcast, just the broadcast signal. We were clearly shown a mismatch between what was happening in person and what the broadcast showed happening.

(I made some tweets about this whole thing: 1, 2, 3, 4.)

Defeating this plan took multiple things and would not have happened without Hajime's effects on everyone, especially Rui. OD needed to defeat Berg-Katze to recover Rui's NOTE, but that wasn't enough by itself; Rui had to reach a point where he would offer the clearly dangerous power of Crowds to everyone, where he trusted that people's potential for good would overcome the clear possibility of even more chaos. It was a brave gamble given that it amounted to pouring more potential fuel into a burning fire.

(How I regard the 'gamification' of GALAX and its users is sufficiently complicated that it calls for another entry.)

On OD: I have no idea if he's supposed to be dead or not. On the one hand he does collapse from his injuries and doesn't appear in the epilogue. On the other hand, his visible injuries don't appear to be life threatening, Utsutsu was presumably available for healing, there are no visible signs of mourning in the epilogue, and other characters don't appear in the epilogue either. I'd like to convince myself that he survived but I'm not really able to do so.

Similarly, I have no idea if the fallen Crowds' people from Rui's fight with Berg-Katze eventually recovered. I'd like to believe they did but I don't think we have any evidence about it one way or another.