I see several problems. Granted it's not even a full treatment but...
Superman: The Man of Steel
TMS started just a few years after the incidents that we saw in Superman Returns. Kal-El is doing what Superman does best, Lois Lane is raising her kid Jason, who of course is Superman's child and the world is getting use to having Superman back.
Now there are storyline threads that go back to Superman Returns, one is the on going plot of Superman's original reason of going back to Krypton. He has always wondered if he truly is the last Son of Krypton.
Remember new Krypton that Lex created with crystals he stole from the Fortress of Solitude and Kryptonite that Supes launched into to space that nearly killed him?
So new Krypton continues to grow in space and has become an almost perfect sphere. It is now the size of a small moon.
Besides giving Humans something to admire at night, Earth new satellite has also brought some unexpected attention from a galaxy far, far away.
A massive spaceship arrives Earth's orbit, Superman flys up to meet the spacecraft and we are introduced to our out of this world visitor.
I assume this is all in the first 10-15 minutes of the film. Fair enough.
Superman quickly finds out that our visitor is also a Kryptonian survivor who has been traveling the known galaxies and was able to detect Kryptonian technology thanks to our new green/black satellite that has started to orbit the Earth.
Superman finally has found a Kryptonian buddy and starts showing him around the planet, a planet full of problems, disease, famine, crime and nations at war with each other.
Our new Kryptonian friend asks Superman why, with all his power, is he not changing the world for the better. Why is he not getting rid of famine, disease and war? Of course fans know that Superman has always been told, or better said instructed, not to interfere with Earth's development.
Superman explains that he is not allowed to interfere but his Krypto buddy tells him that with their powers they are required to "interfere," Superman disagrees.
Krypto buddy decides to take charge and starts "interfering" from day one. One of the first things that he does is get involved in a political mess that is heating up between two third world nations.
War breaks out between these two nations but before any real battle breaks our Krypto buddy interferes and lays waste to these two Armies.
Early big action sequence - in which Supes does what? Stands by and watches? "Krypto buddy lays waste to two armies" - that's a lot of people dead.
He declares to the world that he will not allow anymore wars and/or the destruction of our planet. He is declaring a "War Free" planet and for those who disagree he will have to deal with them.
The major nations of the planet applaud his actions and all agree to an immediate worldwide peace. In return he promises to share technology, fight hunger, famine and disease.
The population of the world rejoices and any small pockets of resistance is quickly squashed by Krypto buddy or even the world governments.
The world rejoices at an all-powerful dictator enforcing peace at the end of his heat vision? WTF?
Superman has now become a pariah, the way the world sees it, he has been here for years and had kept technology that could have saved many of the worlds problems.
Superman starts getting a bit suspicious of Krypto buddy and decides to go talk to him.
TALK to him? He's just murdered numerous soldiers, declared himself dictator of earth and promised to end hunger, famine and disease, um, how exactly? Is he going to become a farmer and a doctor? These aren't exactly problems to be fixed by being able to lift heavy objects. Okay, share technology... nifty Kryptonian technology which apparently has the amazing ability to - grow big crystals when added to water? Fabulous!
I know comic book movies can gloss over logic, but, seriously - how is the movie going to show him spreading the knowledge to build the technology to solve problems like famine and disease? Will it stop for 10 minutes in the middle to show Barniac's "Solve all the World's Problems University" being founded?
He goes to his spaceship and has a revelation. This massive ship is full of hundreds if not thousands of identical bodies aboard, yep, clones of Krypto buddy, in stasis.
So Superman digs a bit more inside the "computer" system, which is familiar to him since it's Kryptonian technology just like the Fortress of Solitude.
Superman finds out that Krypto buddy is actually an artificial intelligence from Krypton that has evolved since the destruction of their world.
He escaped Krypton just like Kal-El did and his real name is Brainiac. He has been going from planet to planet, taking their technology, helping these worlds reach a relative perfection and then he destroys them and moves on.
Here's my biggest problem. Braniac perfects worlds - and then destroys them. And why does he destroy them? Because that's what eeevvvvilllll villains do?
Superman also finds out that he was actually responsible for the destruction of Krypton and tries to warn the leaders of the world but is confronted by Braniac. A massive battle ensues and Superman is about to defeat his foe but right just before Brainiac downloads his conscience into one oh his other clones.
Superman realizes that he must destroy this massive ship along with all the clones aboard. After another massive battle he is able to disable the ship, destroy the clones and the new Braniac but right before the ship is destroyed the Braniac main frame does a local search for another body that he could download in to, it has to be Kryptonian, and he finds another one on Earth, Superman's kid
So Brainiac uses Kryptonian technology and beams/download itself into Jason's body and this causes causes him to age and grow into a full adult but with Brainiac in complete control.
Superman realizes what just happened and rushes to confront his very own son who is now possessed by Brainiac.
Is Jason still there or is it all Brainiac? It's all Braniac and Superman knows what he has to do, he must defeat Brainiac at all costs or the planet and it's inhabitants will be doomed.
It's a battle between two gods but Superman has already been run ragged and beat down pretty bad in his previous battles of the day. Brainiac has the upper hand and Superman is trying to not to do any permanent damage to Jason's body.
Every time Brainiac is defeated in the past he simply tries to download to another clone and leaves that body completely brain dead but with no other bodies left, will Jason survive? The answer in no.
There is a Christ like metaphor here. Superman has to sacrifice his own son to save humanity.
There are still plenty of holes left in this story, we were not privy to all the details but this is the bulk of the info we received.
I can't even get into the whole Superman sacrifices his son (who has gone the way of so very many heroic offspring - directly into plot device territory) because the first half of the plot doesn't make much sense.