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.
Fan Dumb: Some fans claimed that Superman was acting tyrannical, beating the crap out of the Elite despite the fact that most people agreed with them. Never mind that Superman spends the whole movie trying to explain peacefully why they're mistaken and that the Elite tried to kill him before he decided to really get violent. Rather amusingly their criticism of Superman for playing by the same rules of the Elite echo Manchester Black's hypocritical rantings during the finale.
Of course, the fact that he didn't strip them of their powers in the original comic, yet does here, means that there is some nugget of truth in that.
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.
After watching Superman explain why he would never kill, it can be quite jarring to see Man of Steel, where Superman snaps Zod's neck. There's also a stark contrast between Superman trying to limit collateral damage until he begins playing by the Elite's rules, and the level of destruction caused in the climactic fights in Man of Steel.
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.
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.