(at around 39 mins) When the airliner crashes it wipes out the cars behind the first row, and cars are thrown about and chaos begins in the scene. When the camera follows the main character, you can see the shadows of people sitting in the first row of cars like nothing happening. The digital fire is easily seen covering up anything behind it.
In 1959, some 50-star flags are seen. The 50-star flag was not introduced until July 4, 1960. The scene should have used the short-lived 49-star flag of 1959-60, although most people didn't replace their 48-star flags until the 50-star flag came out.
(at around 2 mins) In the 1959 classroom scene, there are a number of flags above the chalkboard, where the white-blue-red Russian flag (used by the pre-1917 Russian Empire and post-1993 Russian Federation) can be seen amongst them. In 1959, Russia was the U.S.S.R. which used the yellow hammer and sickle on a red flag.
In John's lecture on Determinism/Randomness, what he's actually describing are (anthropic) teleologism and metaphysical naturalism - both descriptions being causally deterministic. Only when questioned what he believes does he describe a random element.
(at around 1 min) At the beginning of the film, when the teacher is calling the children in from recess, several children are walking up the steps to the school and walk past the teacher. The teacher then calls for Lucinda (who is standing off by her own), and there's a cut to a medium shot of Lucinda facing away from the camera, and 3 of the children who had walked past the teacher a few seconds ago are now again walking away from Lucinda and toward the camera (a kid in a blue sweater, a chubby kid in a short sleeve striped shirt, and a blonde girl wearing a white dress with an orange sweater).
(at around 38 mins) When they first spot Flight 74, John and the state police officer are both looking back along the centerline of the highway - 90 degrees from the jet's actual line of flight, which crosses the highway at a right angle. At the beginning of the next shot, when the jet appears in frame, John's head is turned 90 degrees to the right.
Midway through the movie, as the sheet of paper with the numbers on it sits on a desk, there is a small wear tear at the bottom fold/crease. Later shots of the same sheet of paper show no tear at that crease.
In the opening classroom sequence, the clock on the wall behind the teacher remains at 1:10 throughout the majority of the scene, despite the obvious passage of time. The next time the clock is seen the hands have jumped to 3:00.
(at around 18 mins) When Caleb first removes the numbers from the envelope, we see the end of the sequence of numbers. The final two numbers on the page are clearly threes (rounded on the right edge), not the backwards E's seen in the rest of the film.
(at around 1h 6 mins) When John is driving Diana and the kids in his car and explaining how his wife died in a fire, his hands on the steering wheel aren't moving. The wheel is frozen in one spot, which would not keep the car on the road.
When John erases Caleb's homework from the dry-erase board so that he can write down the numbers, he leaves some of his son's vocabulary/spelling words on the lower portion of the board. Each time we see the board after that, the first vocabulary word varies as to how much of the word remains after the erasing.
When John is teaching at MIT in the beginning of the movie, there is a female student in the front row, to the left of John. In one shot she has her arm up and is playing with her hair. In the next shot she is in a completely different position with her arm down. Then, it goes back to a shot of her with her arm up.
(at around 5 mins) When the time capsule is being buried at the beginning of the film there are three male teachers standing to the right of the stairs. One of the men is standing more to the left than the other two with one of them in front of the other. When the shot changes to the rear all three men are standing in a line.
When John first sees the pattern on the paper, it is the 0911012996 that catches his eye. This would be incorrect because 2,996 was the total deaths on September 11 from all 3 locations (New York, Pentagon, and United 93) yet the paper gives GPS coordinates for individual locations.
(at around 1h 30 mins) When Diana walks into the convenience store to watch the Emergency Broadcast Transmission, someone is holding a bag of Smith's potato chips. This is an Australian brand and is not sold in the United States.
(at around 52 mins) While getting a drink on the museum roof, the skyline is completely impossible, showing the Prudential Building to the left of the Hancock Tower, places the viewpoint in the south end of Boston, behind Copley Sq and on Hunnington Ave. However the scene also shows buildings in the middle of the frame, the custom tower and other downtown Boston skyscrapers. This perspective would require them to be in downtown Boston, and even then you would not be able to see either the Prudential or the Hancock.
The NYC subway station (filmed in Melbourne, Victoria, Australia) has an interior, cars, and a painted plywood sign unlike anything in New York. After the subway accident, there are types of fire trucks that are not used by the New York City Fire Department.
(at around 54 mins) After John and Diana have walked out of the museum into the car park, on the ground near the cars you can clearly see that the arrows on the ground direct the cars to keep on the left side of the road, as the scene was filmed in Melbourne, Australia. However, in America, cars are obviously driven on the right-hand side of the road.
(at around 55 mins) When John enters the coordinates of the impending NYC disaster in Google Maps he enters the longitude without a negative sign, which should have brought up a map in the eastern hemisphere.
(at around 1h 11 mins) In Lucinda's house in the woods are newspaper articles attached to the walls, depicting past tragedies. The last one tells of a mine collapse in East Germany that killed 238 people. It was supposed to have happened in Luisenthal. The incident did actually happen, but Luisenthal is in Saarland, which is the most western part of Germany, which back then was a different country. Also the number of people who tragically died was higher, amounting to 299 persons dead.
(at around 1h 30 mins) When the emergency alert comes on at the convenience store, three short warbling beeps are heard as the message begins. These tones are encoded messages to broadcasters regarding the message enclosed in the emergency alert; however, the short tones heard in the film indicate the end of an emergency alert, not the beginning of one. Opening tones are much longer.
In the subway crash, the train takes out a large number of pillars. In a real subway station, they would have substantial concrete or steel girders inside them. Subway trains, however, are thin-walled structures, with the only real strength being in the bogies underneath. It's just not realistic; the train should rip apart or fold around the first pillar it meets. And, with all those pillars removed, why doesn't the ceiling collapse?
(at around 1h 30 mins) Towards end of the movie when the cell phones are not working, Caleb calls his dad, John, from a payphone at the gas station and John answers his cell phone. However, Caleb calls John at night, while the solar interference happened in the daytime. There would have been less interference at night.
(at around 1h 30 mins) When Diana is driving away from John (and toward the caves) she tries to call John on her cell phone. It says "no service" when it clearly has all bars of signal strength. However, while the cell phone has full bars, the network may be jammed, on certain carriers the bars turn to a different color when this happens but remain at full strength.
(at around 40 mins) The crashed plane is identified as a "commuter jet flying out out of Pittsburgh". The plane is carrying a registration that starts with EC-, denoting it is actually registered in Spain. The aircraft could've been leased from a Spanish airline and kept its original registration number.
(at around 8 mins) When John and Caleb are looking at Saturn, they appear to be looking through a "finder scope," a small low-power telescope used to help point the main telescope. The real finder scope is visible on top of the main scope; what they are looking into is an eyepiece extender (actually a prop made of metal and painted wood) which swivels the eyepiece to each actor's height and allows much better camera angles.
(at around 18 mins) When the fifty-year-old time capsule is opened, the envelopes are handed out to the elementary school students. The envelopes and paper inside them may appear as though they are new, but they have been sealed in an air-tight container that would vastly limit the degradation of the paper inside.
The time capsule was apparently sealed only with a screw-on lid and was just placed in a hole in the ground, left uncovered and unsealed except for a manhole which was itself unsealed (and manhole keys are held by just about every construction and utility company, no matter how small they are). While we, the viewers, know the number sequence to have genuinely been put in by Lucinda, 50 years ago, to any of the characters in the movie it should seem like an obvious hoax made after the "future date" disasters happening. That John, someone who apparently does not believe in determinism, is so readily convinced that the paper was written 50 years ago seems more than a little implausible.
Since the aliens can, and do, take the children themselves, without the parents' help and indeed in spite of interference from them, there appears to be no reason for the encoded message. If so, then Lucinda (who has left the encoded message) suffered for nothing. The message does not trigger Caleb's ability to hear the whispers, as the girl Abby hears them, too, and without benefit of such a trigger.
The latitudes and longitudes in Lucinda's letter do not specify whether they are North, South, East or West, but John assumes they are North and West. The numbers alone could each refer to any one of four spots in the world, but this vagueness is never addressed.
(at around 38 mins) The windscreen wipers on most of the vehicles caught in the traffic jam on the freeway before the plane crashes are sweeping the windscreens as they would on right hand drive cars (as in Australia), that is from right to left as seen from the front of the vehicle. The windscreen wipers on left hand drive cars (as in the U.S.A.) sweep the opposite direction.
(at around 58 mins) When John goes down into the subway station in NYC at Worth and Lafayette, there are apparently lengthy escalators. Other than in the WTC itself going down to the PATH trains to NJ, there are no escalators than long in that area.
(at around 13 mins) In Dr. John Koestler's classroom scene, camera movement shows chalkboard writing not moving in sync with surrounding chalkboard smudges, which is highly suggestive that the writing was added in post-production.
(at around 27 mins) John shows Phil a printout of an article reporting the 10/27/2008 hotel fire in which his wife was killed. The first page lists the current top searches as "Finance Overhaul Autism Robert Mugabe Tibet Ukraine Pope Benedict XVI Climate Conference Baghdad Stonehenge Baseball Season," indicating that the page was made from a real news page published in April 2008, when this scene was filmed. The print date in the corner of both pages is 8/04/08 10:15 AM, indicating that the prop page was reprinted much later to re-shoot the closeup.
The goof items below may give away important plot points.
After John finds the last coordinates and discovers Diana has left with the children, the tailgate to his Ford is down. Throughout the rest of the movie, it alternates between being closed and missing.
In the subway, John is seen running at the woman with the baby, behind him you see 3 people go flying into the side of the subway cart when the derailed one hits it. At the end of the crash it's only John and the woman in the car.
When Diana is being worked on in the ambulance by paramedics, it is obvious that it is a "right hand drive" vehicle due to filming in Australia. US ambulance patient compartments are configured to have the "jump seat" directly behind the left hand driver or centered, this positions the stretcher on the left side of the vehicle (or centered), to accommodate a right hand "side entry door".
(at around 1h 50 mins) The line of solar flare destroying Manhattan is shown from many angles as moving from south to north, but the shot where the MetLife Building and Grand Central Terminal are destroyed shows the fireball destroying those buildings from north to south. The camera angle is from across the street from the South Entrance of Grand Central looking north and the fireball comes up from behind them. A few seconds later, when Times Square (just a few blocks away) is destroyed, it is shown "correctly" from south to north.
(at around 1h 40 mins) When John parks on the river bed near the mobile home, just prior to the arrival of the alien ship, 2 deer are seen running past, a buck and a doe. They are clearly not whitetail deer and look more like red deer (an imported European species) that are found in Australia. Whitetail deer are the only deer species in the U.S. Northeast.
(at around 1h 35 mins) When Diana is in the back of the ambulance, she is wearing a bra as the EMT's apply the defibrillator. In a real emergency, all clothing is cut from the victim's chest before being shocked, especially a bra that would likely contain metal hooks and under wire.
When Lucinda wrote the numbers in 1959, she appears to be aged 8-10 yrs old. When she dies in 1988, a newspaper reveals her to be 33 yrs old. Even though this would mean that she had only aged around 25 years in a 29 year period, she may have been older than she looked in the opening scenes of the movie. Also, it is worth noting that newspapers regularly get such information wrong.
(at around 38 mins) When John is speaking with the police officer in regards to the situation on the freeway, the officer notices something coming from directly behind John. The plane is actually coming from the officer's right (John's left) and would not be visible directly behind John.
During the plane crash when the camera pans to a group of survivors struggling away from the plane debris a man is standing far ahead of the group and engine. When the engine explodes he is far away from the blast, but visually in front of it, and he simply disappears in one frame.