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The whole scene where Superman saves the boy at Niagara Falls is several bangers for the price of one:
First, there's the obvious fact that both the boy and his mom are each firmly holding an Idiot Ball. The boy playing on the opposite side of the rails looks like he should be more than old enough to know better. And the mom? She just glances at him when he's fooling off risking his life and says "oh yeah honey, that's nice.". Horrible parental supervision is an understatement.
The reason Lois begins suspecting Clark is Superman is not only because she sees him while Clark isn't in the area, but because she wonders why he would suddenly show up in the middle of Niagara Falls of all places. Excuse me, but didn't Superman just save you up in Paris just a little while ago? And wasn't he seen in California before that (in Superman I)? Why would it be any more shocking that he also shows up in Niagara Falls?
Clark gets his own idiotic moment when Lois tells him what happened and he plays dumb, saying that he didn't see Superman in the area at all. Considering that he was supposed to be outside at a refreshment stand where everyone in the area could clearly have seen him fly away even if they didn't view the rescue beforehand, couldn't he have said something like "Oh yeah Lois, I saw him fly away while I was getting the hotdogs! What was he doing?" Nope, instead he pretends to be the one person in the entire area not to notice his alterego even though the only way that could happen was if you were blind. Yeah, that doesn't sound suspicious at all Clark.
Clark Kent? Who's that? The film features Clark maybe 5 minutes. In addition, no one, repeat NO ONE seems to notice or care that Clark Kent and Superman disappeared and reappeared at the same time. Not even Lois who in Superman II was obsessed with proving Clark = Superman.
Lex Luthor is released at the beginning of the film (offscreen) because Superman failed to show up to Lex's appeal hearing. The only problem is that Superman had (by the time the movie begins) already been gone for close to 5 years. What kind of court relies on the testimony of a superhero who hasn't been seen by anyone in years? And when did an appeals court suddenly require witnesses to come forward?
For those who don't know civil procedure, just about all the evidence seen by an appeals court was already introduced at the trial level, and new evidence is actually inadmissible except under extraordinary circumstances after the initial trial.
After deciding to sneak aboard Lex Luthor's boat to find out what caused the blackout in Metropolis, Lois Lane not only takes her child along with her, but doesn't bother to take her cell phone in case she's in danger. What an Idiot.
Thom Holbrook wrote an essay pointing out that Superman is dumber than a bag of hammers in Returns.
The big inspiration for Superman Returns is when Superman and Lois had sex, what if he got her pregnant? Thus the need for him to be gone five years so that he could return to discover he has a son. That also means that, clearly, Superman left before he knew Lois was pregnant, we can assume he left shortly after Superman II. Really shortly. He's Superman. He would be able to see Lois was pregnant very early on with his vision. Lets say he leaves… two months after the end of Superman II. So in Superman II he painfully learns that he must put the needs of Earth ahead of his own personal desires. He apologizes to the President for being away so long (he was gone maybe a week or two) and that he won't let him down again. Then two months later he leaves Earth without telling anyone on a personal five year long wild goose chase. He also leaves without covering his bases. He doesn't secure the dangerous tech in his Fortress of Solitude. He doesn't make sure his departure won't result in Lex Luthor's release from jail. He doesn't even apparently warn the President he's leaving. His actions fly in the face of everything he learned in Superman II and everything he swore to do. Dumb as a bag of hammers.
The ending of the movie has an Inferred Holocaust, with a large chunk of Metropolis annihilated due to General Zod and the Kryptonians' terraforming machine before Clark shuts it down for good. Yet, in the final sequence, things are back to normal and Clark is going to work at the Daily Planet for the first time like it's any other day - streetcars are operating, passengers are standing without much reaction, etc. You'd think that the destruction and death of so many civilians (either caused directly by the machine or its resulting damage (i.e. collapsing buildings) would be front-page news for weeks, but it doesn't get any mention and we're left to assume that they handwaved the consequences. Really?
Forget any reasons given in the comic book; there is no good reason given in this film as for why the Kryptonians couldn't evacuate at least some of their people off the planet. Krypton has space colonies, interstellar spaceships and even the god-damn prison in orbit that they could have gone to. On that note, Zod's punishment for high treason and murder? He gets to live whilst everyone else commits suicide! It's lazy writing at it's finest: The writers need Superman to be orphaned and sent to Earth as the Last Son of Krypton and they need Zod to follow and become the Big Bad; so it just happens regardless of whether it makes sense or not.