The PA at the airport in Berlin welcomes the passengers to "Berlin International airport". However, Berlin does not have one, but two international airports, Tegel and Schönefeld (and at the time of the movie, also Tempelhof), so the PA would have specified which one.
As the plane is speeding down the runway in Berlin, Kyle is seen buckling her seat belt and a flight attendant is walking down the aisle. Air travel regulations require that seat belts be fastened before aircraft taxiing. Flight crews are supposed to be seated and buckled in as well.
When the airplane is about to land, some passengers stand up. A father takes his camera and says to his son, "Sit back," and takes a picture with flash, however if you use flash in front of the glass the light will be reflected and the picture will be no more than the flash light.
When Kyle goes to talk to the captain through the cockpit door, the air Marshall pins her to the door. Her mouth is pressed to the door near the peep hole but in the next shot, she is to the left of the peep hole.
After Kyle is knocked down by the Arab, she has a small gash on her cheek. When she's asking the stewardess later what part of the plane she searched, there is no sign of any injury. The gash resurfaces later.
Early in the movie when Kyle is leaving with Julia her hair is in a tight bun with no wisps loose. In the taxi there are wisps of hair down, then at the airport her hair is back in the original (no mess) bun again.
When Kyle goes below deck, to look for Julia, when she opens up her husband David's casket his right foot is straight up and down and his left foot is tilted to the left. Then when Carson goes back down to the casket, after detaining Kyle, to get the explosives both David's left and right feet were straight up and down.
In the exterior shot at the airport you can clearly see that the "Leipzig/Halle Airport" signs at the jet bridge are pasted over because the adhesive foil color does not match exactly the color of the jet bridge.
At Berlin "Alexanderplatz" station Kyle and her husband enter the subway line U5 driving to the eastern suburb of Hönow. When they leave the train it is the subway line U6 at "Platz der Luftbrücke" in the southern district of Tempelhof, which is in the opposite direction. There is no direct connection between both lines.
Over the course of the movie, Kyle's search for her daughter takes us further and further into the various compartments and holds of the aircraft, eventually taking us into areas far beneath flight deck. The problem here is with the layout of the bowels of the aircraft. As shown, this airliner's computer room is large and cavernous, with much empty and unused space. In reality, virtually every square inch of any passenger liner has a purpose, and with the exception of passenger and crew areas, every other part of an airliner is unbelievably cramped, filled with cargo, electronics, hydraulics, or emergency equipment. Such a waste of space, as depicted in this film, simply wouldn't exist.
The avionics computers shown in the film appear to be an array of Cray supercomputers in the circular configuration typically seen in a supercomputer lab. In reality, avionics computers are small, ruggedized embedded systems which are distributed throughout the plane. Avionics computing requires highly reliable redundant systems, not massive computing power.
When the airplane is shown being "de-iced" before takeoff, it is obvious that the trucks are simply spraying soapy water all over the airplane. Real de-icing/anti-icing fluid is applied only to the wing and tail surfaces, and would not be wasted on the passenger windows. Furthermore, real de-icing/anti-icing fluid (treated propylene glycol) is pinkish, gooey, and very expensive.
There are no overnight flights between Berlin and New York. Due to time changes, if a plane left Berlin at, say, 8pm, it would arrive in New York at approximately 1am. Flights from Europe to the east coast virtually all leave in the morning to early afternoon, and arrive in the States afternoon to early evening.
The production designers did a rather poor job with the design of the fictional airplane. Besides the large amounts of unproductive empty space already noted, and the mismatch between number of engines and cockpit instrumentation, there are several other glaring mistakes. First, the aircraft fuselage structure is depicted as a tubular metallic design like buildings on the ground, when in fact all modern commercial aircraft use monocoque structure where the skin is the main strength element. Second, the heroine messed with an open panel consisting of many switchboard-like cables terminated with phone jacks like an old telephone system; no aircraft would use anything like this in the general or specific sense. Third, cabin lighting is shown being on the wall shining into passengers' eyes, instead of overhead.
The space between the windows appears to be much larger from the outside than from the inside of the plane. Compare the image from outside of the plane of Kyle and Julia watching the casket ready to be boarded to the interior shots of the space between the seats and windows.
When you see the shot of the landing gear touching down on the runway on landing, notice the aircraft does not flare. (Flaring an aircraft means to bring the nose up on landing so that the main landing gear touches down first, then the nose gear. If a plane lands as shown in the movie, there is a risk of the landing gear collapsing, causing the aircraft to crash.)
At one point Kyle is in the galley with most of the plane's crew (at least all the ones we've been introduced to) and its captain. The camera takes a rotating view of Kyle and at the end of its rotation on the left-hand side, the smallest bit of "untreated" green screen is visible.
The goof items below may give away important plot points.
At the end of the film the plane makes an emergency landing in Newfoundland, Canada. For some reason the FBI is in charge at the airport. However, the RCMP has jurisdiction in Canada, not the FBI. Also, the FBI claim that they are holding the coroner in Berlin, but they have no jurisdiction in Germany.
After the plane is evacuated, Kyle figures out the scam and assumes the role of hijacker in order to thwart the real hijacker(s). She appears to have two hostages, yet no one attempts to initiate hostage negotiations with her from outside of the plane during the whole subsequent cat-and-mouse scene. Also, one of the "hostages" leaves and law enforcement doesn't receive her.