When Victoria reports that Jackie went off comm in grid 17 and requests a drone, Sally responds by saying that she will send a drone to grid 22.
After Jack 49 gets the medical supplies from Tower 52, he is surprised by Victoria 52. During their conversation Jack 49's rifle sling changes position multiple times covering up different portions of the 49 embroidered on his suit.
When Jack unloads his motorcycle from the aircraft it has sport bike street tires. When he rides away on the dirt it has knobby dirt bike tires. Later when the "Scavs" return it to him outside of the bunker it has street tires again.
When Jack refuses to help sabotage the Tet, Sykes shoots Jack in the chest, leaving a burn hole in his uniform. After Jack leaves, evidence of the the burn hole is no longer visible in Jack's suit..
When Jack is investigating Drone 172 in the library sinkhole, the cable snaps and he falls. The sling on his weapon is visible during the slow-motion scene, but it is no longer on the weapon when it falls off the ledge a short time later.
At night, a clear view of the exploded moon is visible in the night sky. With the debris caused by the explosion raining constantly into Earth's atmosphere, the night sky should be filled with "shooting stars" for the next several thousand years, especially in the deserted Earth's non-light-polluted evening skies.
At about 34:00, when Jack first goes to the house by the river he puts a long-play album on the stereo and plays the first track on one of the two sides. The song which starts is "Ramble On" by Led Zeppelin. This song first appeared on Led Zeppelin II, and subsequently on some Led Zeppelin compilation albums, but it has never been the first track on any side of a long-play record.
In the flashback scene when the Odyssey is approaching the alien vessel near Titan, the communication with "Mission" is immediate. In reality such a great distance would introduce a delay in both sending and receiving messages. It would take over one hour for a message to reach Earth.
Though it's seen to be much farther away, the sound of the exploding hydro-rig is heard approx. 3 seconds after Jack sees the light of the explosion. This would put the large nuclear blast approx. 3,200 feet (6/10th of a mile) away, not the many miles shown.
The Light and Sound of the exploding Hydro Rig arrive at their residence at the same time, and while light at that distance would be near instantaneous, the sound should have taken at least a minute, if not longer, considering sound takes 3 seconds per kilometer to propagate through air (faster through rock, but their residence was a kilometer or more above ground)
Shortly before the end of the film, Jack listens to the contents of the black box which he found in the crashed crew module with the hibernating "Odyssey" crew members. The recorded cockpit conversation between Victoria and Jack goes on after sealing off the module with other crew members and even continues after jettison of the module. At first glance it seems the cockpit conversation could no longer be on the black box, but the system could have been transmitting the recorded conversation to the crew module with the black box.
The design of the bubble ship resembles a helicopter including a tail rotor, but a tail rotor is provided to counteract the spin that would be caused by the main rotor in a helicopter. The bubble ship has no main rotor, so there would be no need for a tail rotor to counteract spin; however, a thruster on the end of the tail pylon would supply much more maneuverability than using the inboard engines to spin the ship.
When the 3 drones attack the Scavs' cave/dwelling and one hits Jack, throwing him aside, the table he lands on bends at his weight until he falls off, revealing a soft or padded fake table.
When Vika throws the plant off the house-platform, the wind can be heard howling as a storm is approaching (with thunder being heard in the distance). Despite this, Vika's hair in her ponytail never moves indicating the wind was actually only a sound effect.
When Julia wakes up at the lake cabin just after being shot, her hair is long and undone. She walks right out to see Jack and her hair is suddenly braided.
During the opening montage showing the aftermath of the war, the Washington Monument is tilted. The monument was constructed with over 36,000 marble blocks held together only with gravity and friction. There is no metal support structure, and no mortar was used. If the monument were to be tilted, it would fall apart.
Beech says that the bedrock around Chicago spared them from most of the waves and earthquakes. As Chicago is located on Lake Michigan and heavily populated areas cling to 90 miles of southwestern lake shore, and as Lake Michigan 22,394 square miles (twice the size of the state of Massachusetts), there is the likelihood that all of Chicagoland would be wiped out, along with the western shore up to and past Milwaukee, as well as Detroit and the rest of the eastern shore.
The crew spacesuits and the Odyssey flight recorder both use the old (loathed) NASA "worm" logo. This was retired in 1992 when the original "meatball" was brought back, and long before the story's plot begins.
Vika's desk display shows Jack tapping out the word "Paradise" in Morse code to communicate with her, but the actual Morse code letters heard are "a-d-i-s-t-r-a-e-e".
When the three drones descend on the Scav base at the end of the movie, they sweep past the camera as they approach at full speed. The center drone nearest the cameras guns are partially outside and below their housings in this shot, incorrectly positioned by the VFX team.
Jack detects a Scav beacon signal emitted from the Empire State Building that is sending coordinates on Earth to the pre-invasion spacecraft Odyssey. The human survivors tell Jack that they decrypted GPS signals to use this transmission of coordinates. This wouldn't be possible that far in the future because the GPS satellites depend upon ground monitoring of their precise positions and slight changes to their orbits from ground controllers to maintain the GPS satellite coverage. With decades of no human intervention the GPS satellites would have long ago drifted, become out of position, transmitted incorrect signals, and failed from old age.
The moon is blown apart and it is said that this caused problems on Earth such as earthquakes. However, the moon is still there in pieces and its mass and center of gravity would not have changed much. This would not have such an effect on Earth.
If anyone wanted to collect water in this solar system to take to another, it would be far easier to collect solid ice from Saturn's rings (which are 24% water ice) or its moon Enceladus; neither of which have life to be fought, and which are substantially farther from the Sun's gravity, making them easier to remove from this solar system.
Earlier in the movie Vika tracks Jack's movements and even warns him as he approaches the radiation zone and definitely gets worried whenever they lose contact. Later when Jack 49 flies Jack 52's hijacked bubbleship out of sector 52, into Jack's lakehouse oasis in sector 49, Vika 52 neither monitors his stray movements, nor warns him about crossing the radiation zone, nor reports the excursion to the Tet or requests Sally to send drones to scout.
Jack-49's bubbleship is able to travel to his lakehouse as his oasis is within sector 49. But his bubbleship shuts down as it crosses the border into Jack-52's sector shown as radiation zone. Keeping up with these ground rules, when Jack-49 hijacks Jack-52's bubbleship, it should not be able to leave sector-52 in order to travel to the lakehouse oasis that exists within sector-49.