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.
Faux Symbolism: More subtle than most with the Superman-as-Christ symbolism, but Clark tells Lois that someone has to show them that killing and violence at any cost. Lois responds that it means dying for them to understand.
Harsher in Hindsight: Superman's disapproval of the Elite's means in light of Injustice: Gods Among Us which has an alternate Superman using similar methods after a Face-Heel Turn after the Joker tricked him into killing Lois Lane and their unborn child, which in turn led to Metropolis being nuked. The fact that George Newbern reprised the role again in the game adds to the harshness.
You can sympathize with the Elite's motivation during the whole movie, due to Strawman Has a Point. Even after they try to kill Superman, you can, to an extent, feel sorry for them due to how Superman apparently reacts. However, Black does cross it when he explicitly states his intention to obliterate the city in order to escape Superman's wrath.
This is also what Superman believes he would cross over if he behaved like the Elite do. And judging by Injustice: Gods Among Us, he's right.
One-Scene Wonder: Adult Vera. She only appears briefly to hand secret info to Lois.
Manchester Black: People don't want babysitters in spandex to spank them when they're bad. They want surgeons to cut out the cancers that fester in us and make sure they never come back.
This debate is very old. Both sides present valid arguments, but both sides views are also flawed as well. Superman's side was deconstructed in the first half, The Elite's side deconstructed in the second half. While the film does pick Superman's side, in the end, the movie presents valid arguments from both sides for viewers to interpret for themselves. And let's leave it at that.
You might want to consider The Elite forcibly enslaved a sentient being to their will, and said being was suffering And I Must Scream. Superman freed the creature from its torment.
There's also this:
Superman: You can't kill people and continue to call yourselves heroes.
However, that's a classic strawman point. Superman never pretended to write laws, or govern a populace.
Manchester also says that the Elite will be safe from Superman if they are with "the sheep" (that is, innocent people). They're counting on Superman not causing the collateral damage that they have no problem with.