Who edited Zod's creepy broadcast?
Jenny at the Daily Planet mentions that the message is playing via RSS feeds, and so clearly Zod has done research into our ways. General Swanwick is of the belief that whoever is on the spacecraft is looking to make a dramatic entrance, and well, doesn't that video do just that? Zod is playing on our fears, as he wants to intimidate us into giving him the location of Kal-El; that is his whole goal - for us to hand him over. It's scaremongering, and it worked. On a purely superficial level, wasn't the video just cool? Seriously, that eerie screeching, whirring noise when the video first starts - that was brilliant. Can we not just enjoy fun little elements anymore without tearing them down?
Why didn't Zod attempt to trick Superman rather than tell him his master plan in a nightmare / hallucination / psychic invasion?
Zod acted throughout the film with Krypton's best interests at heart. That was his purpose - to protect Krypton. He was a General, a leader. He had honour as a warrior, so lying to Kal-El would achieve nothing and go against his code. Zod was fully fleshed out, he wasn't just your average run of the mill comic book villain. Look at the characterisation, and the reason he didn't lie is plain to see.
How did the military not know where Superman flew his ship?
This point is, whilst not necessarily a plot hole, a genuine question from the film. Bravo! However, can we not just accept certain things in a film without picking it apart? How doesn't Marty McFly COMPLETELY DISAPPEAR the moment he gets hit by the car? It doesn't affect the plot, so while an explanation about Kryptonian cloaking devices or something or other would be nice, is it necessary? No.
Why doesn't Superman go after the giant ship in Metropolis?
The World Engine in Indonesia is working in tandem with Zod's ship (in Metropolis) to terraform the Earth into Krypton. The plan is to use the phantom drive (the energy that creates a black hole basically) in Clark's ship that he arrived on Earth in to create a singularity (a black hole / phantom zone) by crashing it in to Zod's ship, which also has a phantom drive. The collision between the two phantom drives is what will cause the phantom zone to open up and suck Zod and company back in to it.
The reason Superman goes to the World Engine is because - and he specifically states - if they don't destroy it before they crash the two phantom drives together, then the W.E. will continue to increase the gravity field from the singularity. Which basically means the Earth goes with it.
Remember when Superman caught Lois after the crash of the plane and you could see Superman sort of fading, as the other Kryptonians had when they were being sucked in to the black hole? Had the World Engine still been around, the 'event horizon' would have become larger and larger, taking more of Earth with it. That's why Colonel Hardy waits, and again specifically states, that he cannot attack Zod's ship until Superman destroys the W.E.
Also, even if that wasn't the case, should his plan have been to attack and destroy Zod's ship first, thereby giving several Kryptonians nowhere to go but the streets of Metropolis and almost certainly preventing Superman from going and attacking the World Engine. That would have been a terrible plan.
How many people would have lived if Superman simply never existed?
Interesting question. I don't agree that Superman is responsible, however a point has been raised: "Is Man of Steel the only superhero film where every single threat would have been resolved peacefully if the hero simply wasn't there at all? Well let's take a look at a few recent superhero films...
The Dark Knight: The Joker exists purely as a reaction to Batman, and Two-Face exists because of The Joker, ergo the entire threat of that film is caused by Batman.
The Dark Knight Rises: The League of Shadows' plan to destroy an American city with a nuclear bomb is born purely out of a reaction for revenge against Batman.
Iron Man: Obadiah Stane only becomes the Iron Monger because of Tony Stark. True his nefarious weapons scheme was already in place, and he did try to have Tony killed, but his rise as a super villain only comes about due to Tony becoming Iron Man. And essentially had Tony not been born anyway, Stane wouldn't have any Tony Stark to dislike.
Thor: Loki attacks Earth because of Thor, and is jealous of Thor his entire life. Had Thor not been born, well, no evil Loki.
So, to that point, no it isn't.
Why does young Clark Kent play as Superman?
I don't think Clark is 'playing superhero'. That's what it may look like to US, the audience, but think about it from the perspective of the characters. Superheroes don't exist in this world, but human civilisation does. Our real world history does: the Greeks, the Chinese Dynasty, the Kings and Queens of Britain. A cape has significance - it has a regal quality. A sense of importance, long before the superhero came along. THAT is likely what Jonathan saw in his son. A leader of people, with regalia and honour.
Zod's plan to release the World Engine before killing Superman makes no sense.
The complaint is that Zod was quite the inept General, and that his plan should have been to destroy Superman before he releases the World Engine.
Well, that's actually a pretty stupid plan. See, in the film we are shown that being around a Kryptonian atmosphere weakens Superman. The atmosphere essentially becomes Kryptonite. Around an atmosphere that is based on Krypton's ecology, Superman loses his powers. Before Zod releases the World Engine he asks Jax-Ur if Kal-El needs to be alive to extract the codex from his body, and the answer is no.
Zod takes a second to think, and commands the World Engine be released. Now, here's the important part: the World Engine and Zod's ship work in tandem to create Krypton by increasing the Earth's mass and clouding the air with particulates - creating Kryptonian atmospheric conditions. The effects of this are seen on Superman when he battles the World Engine and is seen and heard coughing and spluttering, as the Kryptonian conditions weaken him. Lois even asks him before he flies away, "won't it weaken you?".
Zod is actually very wise to proceed in this way. Why engage your soldiers in combat with a man they have already faced, and drew a standstill against? They're actually at a disadvantage remember, since none of them have mastered their super senses and adapted to Earth's atmosphere as yet. Zod's plan to begin turning Earth in to Krypton is the smartest choice. He takes his soldiers out of harms way (Earth's atmosphere) and begins turning Superman's advantage in to his weakness.
Play pay attention to the movie. There are genuine criticisms of this film that can be made, but nitpicking and complaining about parts that you just didn't understand doesn't do much for credibility.