When the ships arrive and broadcast the message to the world, multiple cities across the planet are shown, but it is nighttime in all of them.
When Superman has Zod restrained and Zod is trying to kill a group of civilians with his laser eyes, Zod corners them with said lasers to which Superman ultimately decides to break Zod's neck, though he breaks it right rather than left, which means he was twisting Zod's head towards the people rather than away.
On the fishing boat, Clark leans down to pick up some rope that dropped to the deck. Before he reaches, it is a bunch of random pieces, but when he grabs it, it is a coil.
In the debris of Metropolis, one of the destroyed vehicles is a bus, numbered 6370. This same bus appears later in the film right before Superman crashes through the parking lot, completely undamaged.
General Swanwick's aide Carrie Farris is consistently addressed as "Captain" and wears accurate Captain's bars. The credits, however, list "Major Carrie Farris."
A-10 Warthogs do not make strafing or bombing runs so close to the ground. A dropped bomb can explode after hitting a target and take out the craft. It also makes it easier for the ground enemy to shoot at the passing plane.
When using her digital camera in the Arctic, Lois Lane is able to view the liquid crystal display on her camera. LCDs don't work at freezing temperatures, so the display should have been black.
In the oil platform rescue scene, the USCG helicopter refers to itself by its number "6510." However, Coast Guard helicopters are numbered by type. 65 would mean it is an MH65 Dolphin. The helicopter shown was an MH60 Jayhawk (based on the SH65 Seahawk, based on the UH60 Blackhawk). The aircraft number and callsign should start with 60 instead of 65.
As Superman and Lois are in the desert, with the military a short distance off, waiting for Zod to arrive, a sonic boom is heard (identified as such by the subtitle), and Superman announces that Zod is arriving. A sonic boom is only created by something traveling faster than the speed of sound, so no sound from such a source would be heard before the source arrives.
Special forces operators are shown firing fully automatic weapons on board a flying aircraft. This would not occur as even though their flight system knowledge might be limited, they would have been trained to realize that a stray could damage or destroy flight control equipment and cause the plane to crash.
Anyone who lives in Kansas (or any other state in "Tornado Alley") is taught that hiding under a bridge or an overpass in the middle of a tornado is likely suicide because of the uncontrollable debris fields & random possible funneling effects, which makes the winds even stronger, sucking people out to certain death. Jonathan Kent would have known this, and it is unthinkable he would tell others to hide under the nearby overpass.
However, while this would certainly be true in modern times, the scene in question takes place in 1997, as shown on Jonathan's tombstone. As mentioned in the Trivia section, overpasses were still considered safe in the 90s because of a news crew that famously escaped harm underneath one, and it wasn't until 1999 that the National Weather Service advised strongly that people avoid overpasses during tornadoes.
However, while this would certainly be true in modern times, the scene in question takes place in 1997, as shown on Jonathan's tombstone. As mentioned in the Trivia section, overpasses were still considered safe in the 90s because of a news crew that famously escaped harm underneath one, and it wasn't until 1999 that the National Weather Service advised strongly that people avoid overpasses during tornadoes.
In the ship Jor-El switches the atmosphere to human so Clark has his super strength back. This forces Zod and his crew to don suits providing Krypton atmosphere, thus killing their super powers. But right after they return to the Clark farm in their suits (Krypton atmosphere) they have full superpowers. This goes on through the the next major fight scene. However, this is due to the fact that Earth's gravity is weaker and has less pull on Kryptonian bodies.
During the tornado scenes the trees on the opposite side of the road are not swaying in the winds.
When Clark is standing under the overpass and calls for Jonathan, we can see that he has fillings in his molars.
Despite all the destruction -none of the characters get any dust on themselves.
At 0:17:30 -water droplets on the camera lens.
At 0:20:26 -the crane has no attachment for lifting the lobster trap.
Nine-year-old Clark wears a towel as a cape. No child would ever wear a cape like that unless they were emulating a cape-wearing superhero - specifically Superman himself. The director's enthusiasm aside, and mindful of the idea that Jonathan Kent could envision Clark's future, there is no rational reason for this.
When Colonel Hardy is shooting at Faora, his Beretta M9 sounds like it has a suppressor on it even though it clearly does not.
The final scene right before the drone "impacts" the road, you can see where they buried the explosive charge and the buttressing in the ground, so nothing would impact the car when it went off.
At one point in the Zod Vs. Superman fight, Superman is, while floating mid-air, knocked out after being shot-put through several buildings. Zod then hits him from below and elevates him towards space at high speeds.
From the looks of it, the two of them go up in a vertical line until they hit a Wayne Industries Satellite. The moment they are going back down, it is most noticeable that they are doing so at a certain angle. It's not straight down at all.
Even when they enter the atmosphere and start catching fire, the audience can really perceive them approach the Earth's surface diagonally.
However, when they land, they are still within Metropolis. Much more surprisingly, they're only but a couple of blocks away from where they started--an idea to be introduced by Lois Lane's rather quick appearance. Basing on the distance they traveled up into space and the angle they fell at, Zod and Superman should have impacted at a location miles away from the origin point of the battle, even more so, miles away from Metropolis itself.
When General Zod is speaking to the human race through the television they show several families watching TV at night. When China is dark, the USA, specifically the East coast and Central time zones are daytime and vice versa.
When Kal first meets Zod, there is a scene where Kal has a vision with Zod. During this vision, Kal appears as Clark wearing a Kansas City Royals shirt. It's doubtful he would be wearing that shirt since Kansas City is in Missouri.
When Lois Lane falls from the cargo plane, everything else in the air around her is being sucked upwards, towards the singularity that was created after the cargo plane impacted Zod's ship. She should have been drawn upwards towards the singularity with all the other debris, rather than falling in the opposite direction down towards the earth. Then after Superman flies up to catch her, he himself has to struggle to fly down away from the singularity and get back down to earth.
From 1:23:29 -it is never explained how the image of Jor-El is able to recognize Lois.
During the tornado scene people are abandoning their cars instead of driving to safety.
During the Smallville fight, Superman warns the citizens to return back to their homes to avoid getting caught in between the chaos of the super-powered beings. The people lock their doors and watch as the battle takes place.
The error here is that once the military arrive and detect the presence of the Kryptonians, they immediately resorted to the use of "deadly force," without even knowing if there were still civilians present in the field of battle.
Then, within a few seconds, jets go in "Weapons free" unloading missiles unto a town still filled with people.
Since Superman is indestructible in the presence of our yellow sun, then how can he shave? He appears with a beard in some scenes, then clean-shaven in others. No Earthly razor could remove his beard, a problem which has been used as the driving plot of some of his more humorous comic book adventures.
At 0:49:21 -Jor-El says: "your cells have drunken it's radiation" but drunken is an adjective in the English language.
Clark can't be bothered with menial tasks such as fixing up his foster parent's house.