These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
The cinematics actually do a good job of explaining this: Empire City wasn't treating its homeless well before the blast, and Alden, with his lifelong rage, tapped into something. There's still a lot of bad implications, though, especially since that basically makes Alden Hitler.
The US government, already not very well portrayed in the first game by having bombastic, outright propaganda lie to the rest of the world about the state of the city - eventually bombing its own citizens - graduates into full-on villain in Second Son, doing things like trying to monitor all superheroes. If that wasn't blatant enough, Benjamin Franklin's oft-quoted comment on security and privacy is the game's main quote.
Snipers. You'll often find yourself peppered with gunfire from above when you're exploring an area on the ground (yet another reason to take to the rooftops) and their attacks can whittle away your health while you're trying to focus on guys with rocket launchers or Conduits.
They're extremely annoying when you're doing something else, too - walking around, minding your own business, then BAM! A bullet to your back. The gunfire often draws in nearby mooks, too, and with Dust Men or First Sons, they'll call squads of six or more flying at you like some sort of annoyance squad.
If you're playing Evil Cole, the rock-throwing civilian mobs can be like this, since it's difficult to tell where the rocks are coming from, the throwers don't show up on your radar as hostiles and apparently the city is stocked with dozens of people who could've made a career in the Major Leagues, hitting Cole from the better part of a block away. And to make it worse, in what seems to be a kind of glitch, if you get too close to the mob, some of the members will attack you with their fists, which has the same effect as being attacked by the civilians infected by Sasha's tar, meaning that you can't fight back or do anything other than run for several seconds.
You can fry any conductive item in the game with your standard bolt a couple dozen times, then drain it for way more juice than you'd receive from a power box or light post. Since the bolt doesn't drain any energy, you're basically creating your own electricity. Very useful in tunnels or Alden's tower.
Sometimes easier to come by, you can also do that with corpses. Or enemies.
For the most part, this cannot be done if you haven't restored power to that area of the city. Only a couple of certain structures will let you recycle electricity.
Moral Event Horizon: If you choose to activate the Ray Sphere a second time when given the chance, you become more powerful. However, you kill a lot of people in the process, and your Karma Meter is set to "Infamous" permanently.
Selfish Evil: Evil choices on the karmic path are typically framed in terms of "let/make others suffer for your personal benefit" rather than "let/make others suffer for fun," e.g. forcing a bystander to expose himself to dangerous chemicals so you don't have to deal with those chemicals yourself. The game won't stop you if you choose to electrocute random civilians.
That One Level: "Secrets Revealed". For God's sake, Moya, why did you ask a man on foot to chase down a goddamn helicopter?!?