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.
Harsher in Hindsight: In the Richard Donner cut, the actions that Lois takes to prove Clark is Superman could be seen as insane — jumping out a window so that Superman will save her, pointing a gun (albeit loaded with blanks) to elicit a reaction from Clark, essentially actions that no sane or rational person would attempt (sadly Lois actually did do stuff like this in the older comics during her Stalker with a Crush days). This becomes tear-jerking, when Margot Kidder, the actress who portrayed Lois, would be diagnosed with bipolar disorder after a severe psychotic episode.
Throwing herself into the river in the original Lester cut to make Clark out himself as Superman isn't much better.
The sight of a powerless Clark Kent being beaten up by a roughneck trucker and left barely able to move, along with a shot of him laying unconscious in the Donner cut, becomes harder to watch knowing what happened to Christopher Reeve later in life.
In-unverse example, as Supes apparently didn't remember what happened when he went away for two weeks and promising never to leave again - and then goes on a pointless five year trip to Krypton to determine that the planet really did explode (what?) in Superman Returns.
This Superman realized that having three superpowered villains fighting him in the middle of Metropolis might get a little out of hand, and decided to draw them back to the Fortress where no innocents would get hurt. Cue Man of Steel (Face Palm).
To be fair the Superman from Man of Steel was less experienced and he was thrown into a far more dangerous and intense first adventure than the Superman of the Reeve films.
Narm: Reeve's facial expression as he delivered the line "No! Don't do it! The people!" (Notice how in the preceding shot he looked appropriately horrified at the sight of the bus being lifted, then it looks like he's trying not to laugh and smile as he delivers his lines, then in the third and fourth close up shots he's back to looking suitably horrified.)
And the British boy going, "Please, Mr. General! Please let my daddy down!"
In the Donner Cut of #2 the speech Superman gives to the ghost of his father Jor-El about how Lois is the one thing he truly desires in life, above all else, and you can see Reeve giving it his all, and it's almost touching and poignant and heart-breaking... until you remember that Lois is an illiterate, chain smoking scatter brain who in the Donner Cut threw herself out of the Daily Planet building in an attempt to bluff Clark into admitting he's Superman and then successfully outed him with a fake gun and fake bullets.
Older Than They Think: As far back as the Golden Age Superman comics, Superman had psychic hypnotism powers that he occasionally used on Lois to erase (or prevent) her memories of his secret identity. The "kiss of amnesia" from the Lester Cut isn't anything new.
Only The Creator Does It Right: The Donner cut is generally considered superior to the original theatrical cut; note that Donner directed the first Superman movie.
Romantic Plot Tumor: No matter which version you watch the romantic subplot between Lois and Superman is very iffy - arguably even more iffy in the Donner cut if that's at all possible.
Unfortunate Implications: In both versions - the original theatrical cut and the Donner cut - Superman gives up his powers to be with Lois despite being advised not to do so (by the ghost of his mother Lara in the theatrical cut and the ghost of his father Jor-El in the Donner cut), and shortly thereafter gets his ass handed to him by a dumb, thuggish red neck trucker. Then, adding to his humiliation and despondency, he learns that while he was busy fooling around with Lois, General Zod and his sidekicks took over the world, forcing the now powerless Superman to walk back to the Fortress of Solitude and beg for a means to have his powers restored. What exactly does this say about Superman? That he's basically nothing without his powers? That his heroism ends without his powers? Granted, a powerless Superman wouldn't have done much against Zod and co (unless he happened to have some Kryptonite handy), but it doesn't paint our de-powered hero in a particularly favorable light.
Additionally, after the powerless Clark/Superman gets sucker punched by the trucker he grimly quips that he and Lois will have to hire a bodyguard, to which Lois says "I don't want a bodyguard, I want the man I fell in love with." Clark's response? "I know... I wish he was here." What exactly does this say about Lois and her relationship with Clark/Superman? That she only loved the Man of Steel with the god like powers but not the Nice Guy behind the powers?
What an Idiot: If Lex had any sense of foresight, he would have carried Kryptonite on him. Based on its deadly effect on Superman, you would think Lex would carry around some more in case Zod, Non, or Ursa ever tried to kill him. However, based on his lust for power (he wanted Australia in the first place), it's clear that killing them was not on his priority list. He had good reason to want to destroy Superman in the first film, but in this film, all he wants is control of Australia. While Kryptonite could momentarily take out Zod and his gang, Lex would no longer have any short cut way of gaining his goal, making Kryptonite more of a nuisance than a good thing. Still, it'd be smart to at least carry some in a lead pocket...in the good chance Zod would have tried to get rid of him.
Superman giving up his powers to be with Lois Lane. Even if he didn't have to worry about three super villains from Krypton or roughneck trucker thugs this is just incredibly stupid on his part - and may make his suffering during his loss of powers Unintentionally Unsympathetic.