The Time Travel makes no sense
Isn't it funny how preposterous things we can easily accept, when if we think about them a little bit, they suddenly seem to make no sense?
The time travel method used in this movie is based on some kind of odd premise that a planet's rotation creates / dictates 'flow of time'. This, of course, is a silly writers' gimmick that has nothing to do with reality.
First, time is not localized - it happens 'at the same time' (how else can I put it?) all over the Universe (or at least the 'plane', as in 'physical plane, for example). So changing some cosmic ball's rotation will not affect it.
Second, how is it supposed to work anyway? A planet doesn't just rotate in place, it ORBITS THE SUN.
If Superman would create a bit bigger time difference, it would be more clear that he would ALSO have to tinker with the orbital location, and I don't think even Superman is strong AND intelligent (but he tells the WORLD about his weaknesses!) to be able to do _that_ kind of beyond-Herculean-task correctly.
For example, let's say it's mid-winter in 1978. Superman does his thing, and now we're in mid-summer 1968. However, the planet's orbital location, WHICH DICTATES THE TIME OF THE YEAR did not change. So is it now snowing and dark in mid-summer of 1968, but otherwise, it's the same summer? HOW would this ever work??
Also, did Superman even measure / calculate / research the EXACT rotational speed and angle of Earth before doing this? He would have to restore the Earth back to its normal rotation VERY PRECISELY or time would be sped up or slowed down or whatnot!
If it's even slightly wobbly, time would probably 'fluctuate', as in speed up and slow down, and that would be a huge mess, as we can imagine.
Now, how about Earth's magnetic fields and that kind of stuff? The magnetic field and Earth's rotation are closely tied together, so disrupting the rotation would INEVITABLY cause enormous calamities due to the magnetic poles and consequently the field being disrupted enormously. A pole shift has caused havoc before on this very planet, so Superman should've been a bit more thoughtful and careful about this.
What about tides? What about moon's effect? Same question about the 'seasons', as people would see the moon in the same exact place in the sky EVEN THOUGH the whole planet warped back in time somehow.
Calendars would have to be altered, birthdays changed and so on, it would be an enormous mess! (Even in the version we see, clocks would still be off, because now the sun and moon's movements do not conform to the expected anymore, due to Earth being in the 'same time but different orbital location', so everything would change)
Then there's the whole 'local time' thing - if you jump from 1978 to 1968 and then fly to another planet, is it 1968 there, or 1978? THAT planet wasn't altered, so are you somehow time-warping when you fly between planets? Is this what the movie is telling us, that every planet has its own localized time, so you are timejumping back and forth in time when you travel from planet to another? Why did this not happen with Krypton?
(Or maybe it did, considering that Krypton is supposed to be in ANOTHER GALAXY, and yet Superman just casually tossing an elevator with a bomb in it into space, caused Zod's gang to escape the phantom zone, so Phantom Zone can do warp speed or Superman timejumped or or or..??)
Then there's the pragmatic aspect of 'Superman can fix ANY problem by simply timewarping', so on the surface, Earth would just seem to be completely problem-free, when in reality, Superman is working hard behind the scenes always timewarping to PREVENT problems.
Why would he ever _FIX_ problems, when he could simply prevent them every time? This kind of ruins not only the character, but every single movie/story/etc., because nothing is a problem anymore as long as Superman is alive and can turn back time. Lois falling to the ground? Why painstakingly grab the helicopter and her, when he could just PREVENT that accident from ever happening? Zod was released from the Phantom Zone? Turn back time, move Phantom Zone far away, BANG! Zod never got released.
AND SO ON.
There are _SO_ many problems with this whole time travel thing, it makes even less sense than Superman's 'never-seen-before-sudden-MAGIC-POWERS' this movie shows us, as in the 'forgettance-kiss', the 'let's rip out this S-mark that no longer stands for Superman and throw it at someone'-stuff.
This movie is a mess and an abomination if you compare it to the comics and what the Superman character is supposed to be.
Also, it should be possible that Future Superman comes to prevent the whole time travel scheme, but we don't have to go that far to realize..
..the 'time travel' in this movie makes NO sense!