When Emmett sees the Sea Star boat has reached the island, his shirt is torn on the left side near his waist and the sleeve. When he and Regan are in the radio station in the following scene, the shirt has no rips in it and has become slightly darker; going from dirty-white to beige.
Bear trap scene, as the baby is placed into the basket/baby deprivation box, the injured foot is out of the trap. When the camera cuts back to Blunt, she is releasing the trap. Also, when the foot is first shot going into the trap, it closed below his mid shin, right above the ankle. When released, the trap is higher.
At 1hr 1min mark when Marcus is in the steel mill basement and one of the creatures is coming he picks the box up with the baby in and hobbles towards the boiler chamber to hide, as the camera shows from behind him the door is shut but then the camera view changes to the view from inside the boiler and the door is open without him having time to open it.
At 1:20:58, Emmett taps Regan on the shoulder to get her attention. He taps her shoulder with his right hand in the tight shot, but in the next shot his left hand is on her shoulder.
When Lee is in the shop at the beginning, he picks up 4 oranges. In the next scene he is walking back to the counter with a bag with more than 4 oranges.
The turntable playing "Beyond The Sea" is equipment accurate for a radio station - a Technics SP-10 MKII. However, as part of the major plot point of a months long broadcast of a repeated song/signal, this model of turntable could not have been used as it is a manual turntable and has no automatic repeat function.
In day 1 when Lee and Regan are running away from the monster, it is clearly following them despite other things being much more noisier than them. This is extremely clear when they get out of the pub and the monster seems to ignore the loud trash can noises. While ostensibly correct, the sound-oriented creatures should to be able to focus on their prey despite other noises, presumably similar to how a sighted predator could follow its prey despite seeing other objects and movements.
Before Evelyn and her children encounter Emmett at the steel mill, they walk past a corn field that was planted in neat rows. Since it was Day 474, that would have been from the previous year's planting, Yet the corn field looks like it had been planted in the Spring using farm equipment. It could not have been planted that way because machinery makes noise and would have attracted the monsters to the equipment.
When Regan is in the radio station, "Beyond The Sea" is still playing but the needle on the record is clearly at the end of the song.
The equipment racks at the radio station are full of large scale LED level meters that serve no purpose in this context, at least not as many of them. They are there because they look good on film.
Evelyn tries to kill a monster by shooting an oxygen tank, creating a big fireball. Oxygen itself isn't flammable. It would need a source of fuel to have this effect. The source of fuel is the large puddle of (presumably) oil that she quite deliberately places the tank in moments earlier. You can clearly see the fire spreading across the oil, not just emanating from the tank.
When the fireball (?) flies across the sky at the beginning, people stare but you don't see anyone pulling out their phones to take pictures.
As the camera pans across the personal items scattered across the train station platform, the cell phone has a clean, reflective screen. If it had been in the weather for months, that would not have been possible.
Likely due to VFX changes, the reactions to the meteorite didn't make sense. Krazinski's character say "What was that?" (past tense) while the enormous meteorite is still visible and hurtling through the atmosphere behind him. Everyone else is also just gathering family and heading to their cars as if something had happened, was over, and was no longer visible.
Krazinki's character then asks Cillian Murphy's character if he could ask his brother (in the military) if they were 'doing something'. Again, the SFX clearly shows a large meteorite entering earth's atmosphere. No one would think the military are testing meteorites. So whatever was originally planned to be shown, and was described in the script notes, may not have had the cinematic visual impact of the finished SFX.
When Regan and Emmett reached the island, they seem to be enjoying fire, food, conversations etc while Regan's family is still in a dangerous situation. She didn't even inform her brother who she asked to keep listening to radio station. Even the next morning it doesn't look like they were in any haste to do something to help her family.
In the opening scene Lee picks up 4 oranges and a plastic bag. The next scene shows him carrying a bag with at least 8 oranges in it.
When Emmet pulls Regan onto the bridge the sun is setting behind the Island indicating a western horizon. However the next morning the sun is rising from the same direction while Emmet walks onto the beach.
If the attack took place in their home town / city, and they were overrun on day 1, how did they get newspapers with the reports as shown on the first film? It does not make sense.
As electricity seems to be still running on the island presumably the internet would work as well and people could communicate globally.
When the family leaves the home and the sand ends 18:17, why didn't they just walk across the grass? Walking on the rocks and leaves would make more noise than walking in the nice fresh grass at the side of the path.
If the aliens can't swim living on a boat is a good idea but it doesn't make sense to tie up so close to the dock that the creatures could simply jump aboard.