(at around 2h) On earth, when Hiller tries to fly the alien fighter the first time, he pushes the stick forward and the ship flies backward into the back stop. This teaches him that pulling back on the stick moves the ship forward and pushing it forward moves the ship back. When the fighter is docked on the alien mother ship, Hiller pulls the stick back to back away from the dock. As he should have learned by now, he needed to move the stick forward to move the fighter backwards.
(at around 1h 28 mins) When the first plane fires the first nuclear bomb, you see the pilot is steering his plane away to the left after firing. But, on the radar at the headquarters where the president is looking at, you see the plane making a turn to the right.
(at around 1h 25 mins) When Connie and David argue, David opens the refrigerator door, and we see several items (a milk carton and a few bottles) on the shelves inside the door. When Connie opens the refrigerator a moment later, those shelves are empty.
(at around 53 mins) When Lt Col. Watson is giving Earth pilots the first pre-combat briefing he is wearing Lt Col. insignia. However, when the ground assault by Alien fighters begins, he is wearing Captain's insignia.
The interior of Russell's F-18 cockpit is depicted in two separate fashions when seen from his point of view. At times, his HUD is decorated with a photo of his three children. At others, the HUD is seen accompanied by a matchbook.
(at around 1h 28 mins) When the nuclear missile is launched from the B-2 bomber over Houston, the bomber is within sight of the spaceship. In reality, the missile would be fired from over the horizon, as the B-2 would not be able to escape the shock-wave caused by the detonation if it was within sight of the spaceship.
(at around 50 mins) After Jasmine kicks the door down, in the tunnel, she crouches down & calls Boomer. He leaps in just as the fireball sweeps past. In actuality, they would have been roasted by the fireball going through the open door, consuming all the oxygen as it traveled past.
(at around 49 mins) When Jasmine is running in the tunnel, she kicks open the door just in time to save herself, her son, and the dog. The terrible fireball then goes right by them. They are just inside the open door, with fire and debris flying right past it. While the fire and debris might not spill in, the heatwave would still fry them. It is also likely that the fire would deplete the limited oxygen of the enclosed space.
(at around 1h 1 min) The way Hiller landed when he was parachuting to the ground would have broken his leg with the small round parachute. He should have done a "tuck and roll" to land without injury.
(at around 1 min) The United States flag placed on the moon by Neil Armstrong and Buzz Aldrin is no longer standing. It was knocked over by Armstrong's and Aldrin's take off in the Lunar Module. Furthermore, if the flag was still standing, it would be all-white and not depicting the red, white and blue colors, since there is no atmosphere on the Moon, the Sun would've easily burnt off the colors.
(at around 1h 17 mins) When Steve Hiller first meets the President at Area 51, they shake hands; Since Hiller is a Marine and uncovered he does not salute regardless of whom he is meeting.
(at around 2h 5 mins) When Russell Casse is flying a fighter plane as "Eagle 20", he launches his number two missile or "Fox Two" missile and then attempts to launch "Fox Two" for a second time. "Fox Two" refers to a type of missile (short-range, infrared-guided (heat-seeking) missile - "Fox One", for example, is a passive-radar-guided missile) not to a specific missile on an airplane.
(at around 1h 13 mins) Dr. Okun tells everyone that the aliens do not have vocal cords, yet the creatures seem to squeal and grunt during other parts of the film. However, these aliens are analogous to insects, which do not have vocal cords but have other noise-making organs.
The Roswell Crash Wreckage was taken to Wright Patterson Airforce Base, not Area 51, however, as any military historian and possibly almost all the UFO people know, the debris' trail is lost after Wright Patterson. This is, in fact, the very reason Area 51 became a hotbed of UFO conspiracies, many conspiracy theorists stating that, since it was so secluded, it was the most likely place where it ended up.
(at around 1 min) Since there is no air on the moon the soil should not vibrate from the sound of the Mothership. However, since the movie doesn't explain the kind of propulsion the aliens use this could be caused by the wake of their advanced technological engines.
(at around 2 mins) The opening scene in which the mothership passes the moon heading toward earth, the earth is shown with the southern hemisphere facing the sun - an indication of mid-winter in North America, not July.
(at around 1h 40 mins) The message purporting to be Morse code was gibberish. Additionally, the Morse code keys used to send the message were so far out of adjustment as to be nearly unusable.
There is a common misconception that USA law requires actors portraying military personnel to wear the uniform improperly ("out of uniform") so as to not be "impersonating" military personnel. This is simply not so. 10 U.S.C. 772(f) does authorize the wear of an armed forces uniform by an actor in a theatrical or motion picture production "if that portrayal does not tend to discredit that armed force." SCHACHT v. UNITED STATES was a Supreme Court case in 1970 which found the preceding quote unconstitutional. As such, actors may wear the uniform in a theatrical or motion picture production without fear that it must reflect well on the military. Short version: Any movies which depict improperly worn uniforms can't use this excuse. They simply made a mistake.
(at around 8 mins) When David and their father are playing chess, most of the people in the scene are wearing sweaters or jackets, even though it is July 2 in New York City and the radio says the temperature is 95º F (equivalent to 35º C).
As they run for their lives from the fiery destruction, a group of child extras can be seen laughing and smiling.
David places a Coke can on top of the captured alien ship and asks Mitchell to shoot it off with a pistol. When he tries, the ship's energy shield deflects the bullet. How then did David manage to put the Coke can on there in the first place? The shield is either there or it isn't.
(at around 25 mins) Although it's supposed to be July 2, Steve's morning newspaper is clearly dated "August" in the top right corner.
(at around 1h 40 mins) In the first "RAF" F-16 scene, the tail number on the airframe in the background, WS690, was actually assigned to a Gloster Meteor NF.12 Night Fighter built by Armstrong Whithworth in the late 40s/early 50s.(Page 311 of British Military Aircraft Serials 1912-1966 by Bruce Robertson). Current UK Military serials begin with the letter "Z". Current tail numbers are painted in 12" high white characters on the rear fuselage, not the tail fin. The national markings are also incorrect, if the RAF had operated the F-16 the aircraft would have carried low visibility (pink and light blue) tactical roundels and tail cockades together with squadron markings on the fin and either side of the fuselage roundels.
(at around 4 mins) A US Air Force master sergeant is shown with 6 stripes all down. In 1991 the USAF master sergeant rank changed to 5 down, 1 up, and the old design had essentially been phased out by 1995.
At roughly 24 minutes in, while the alien craft is approaching Manhattan Island, there is a shot from under the Brooklyn Bridge. Off to the left, on the East River shoreline you can see the old Pier 17 building. That building was demolished and replaced by a modern glass building in 1984, a decade before the year this movie is set.
When David and Hiller are approaching the Mother Ship after leaving the Earth's atmosphere there is a "whoosh" sound. That wouldn't happen in the vacuum of space.
(at around 31 mins) When David shows up at his father's house before they leave NYC his father answers the door holding a shotgun. But when he points the shotgun at David it makes the sound of a pump action shotgun, while he is clearly holding a double-barreled non pumping shotgun.
(at around 1h 24 mins) At Area 51, the soldier shoots the alien at point blank range, and two shots are fired. The second shot is heard before he pulls the trigger.
(at around 2h) At the beginning of the battle over Area 51, President Whitmore fires his first missile, which is destroyed by the alien ships shield. As he begins to fire the second, his instrument panel shows he has fired one, and has three left. But when it cuts to the outside his fighter jet, all 4 missiles are still intact. Also the missile fired the second time, is in the spot where the first missile was fired from.
(at around 1h 50 mins) The scientist's mouth never opens when he orders to "open the launch tunnel".
(at around 1h 35 mins) When Levinson is kicking stuff around in Area 51, one of the trash cans is marked "ART DEPT" on the bottom. Area 51 would not seem to have an art dept. Suggestions that ART is a military acronym or abbreviation are amusing, but don't stand as mitigation.
(at around 1h 13 mins) When Dr. Okun is about to unlock "the vault", and says, "the freak show," a crewmember wearing a black and white striped shirt is hiding under the vault's floor, right behind Okun.
(at around 1h 21 mins) Hands can twice be seen moving the tentacles of the alien in the Area 51 lab as it crossed right to left in front of the camera to attack a scientist trying to escape.
(at around 38 mins) When David rings Connie for the second time when he's in D.C. as she walks towards the window, a man is clearly visible crawling along the ground (he is wearing a white t-shirt).
Jeff Goldblum knocks over a bin which is clearly marked Art Dept.
The Empire State Building is incorrectly shown to be in line with the center of a main street.
(at around 2 mins) In the opening shots, the Earth is shown in the background of the alien mother ship. The rotation of the Earth is plainly visible, at about 2 or 3 degrees per second, giving an Earth day of about 2 or 3 minutes.
(at around 1h 27 mins) Captain Hiller "steals" a UH-1 helicopter to go rescue Jasmine. The distance from Area 51 to El Toro is over 750 miles. The UH-1, without additional fuel tanks (which are not shown), had a range of well less than 400 miles, which is about half of what would be required to reach El Toro on just a one-way flight. Without preparations and ground support it would not be possible to make such a flight, especially given the damage caused by the alien attacks.
(at around 2h) Supposedly, the people at Area 51 are safe because they are "deep inside a mountain," but Area 51 (Groom Lake) is not near any mountains.
(at around 27 mins) When he leaves his office, David says that there are roughly 6 hours until the countdown is finished. When he arrives at his father's, the roads are already packed. It takes about 4 hours to drive from New York to DC, in perfect traffic. In reality, they never would have made it out of New York in time.
Major Mitchell reasons that Area 51 will be safe from alien attack since it is deep underground. Except, so is NORAD and the aliens took that out soon after their initial attack.
In what is possibly the most infamous plot hole of the entire film, David manages to "infect" the captured alien ship with a computer virus which disables it's shields. That might have been plausible if the alien ship was running Windows 95 or something other earth-created software, but that's extremely doubtful. Furthermore, David's assumption that by infecting the mothership in orbit with a similar virus would result in disabling all of the alien fleet is even more preposterous.
If the First Lady were in Los Angeles, it is more likely they would have sent her to Edwards Air Force Base or even Vandenberg, both of which are closer to LA than Nellis AFB.
When David figures out that the countdown will end in 6 hours, it's already too late to get to Connie to warn her. It's a 4hr 30min journey by car from NY to DC (in a perfect world).... Add the time taken to ride BY BICYCLE to his father's place, the inevitable delays getting out of NY BY CAR and then again trying to get access to the Presidential circle in the middle of a crisis? Not feasible with the time remaining. David and his father would arrive to a smoking crater in the ground.
(at around 1h 45 mins) Since he did obviously did not pack before leaving the White House, where did Gen. Grey get Marine BDUs on an Air Force base?
(at around 54 mins) When Marines Hiller & Wilder are getting ready to go up the first time, Hiller calls Wilder "soldier." Marines are not supposed to be called "soldier," especially by other Marines. Soldiers are Army.
(at around 10 mins) Farmer Lucas complains to Miguel Casse that his crop is failing because Russell Casse has not dusted his crop. He has a handful of wilted vegetation to prove his case. Dusting is typically for pests, wilting vegetation is typically from lack of water so that would not be Russell Casse's fault for not dusting but rather Lucas' fault for not watering.
(at around 15 mins) General Grey refers to a single AWACS as an "AWAC". The "s" does not make it plural the s stands for System (Airborne Warning And Control System).
(at around 15 mins) The map of Russia shown in "Sky News" (in Russian), shows the city of St. Petersburg as Petrograd, a name used only from 1914 until 1924 (it was called St. Petersburg 1703-1914, Leningrad 1924-1991, and St. Petersburg again ever since.) Other misspellings: Novosibirsk spelled "Novosyoyrsk" (and erroneously described as mountainous), "Fenomen" (phenomenon) spelled "Fznamenon". Inexplicably, the station is called Soviet News, even though the movie takes place some years after the abolition of the Soviet Union.
(at around 34 mins) The address on the letter Steve receives from NASA reads "El Toro, CA 50055" The 50055 ZIP code is actually for Collins, Iowa. The appropriate ZIP Code for El Toro Base (prior to its closing in 1999) is 92609.