After the first FBI agent is shot by Sabrina Ritchie, there is no blood or bullet hole in his seat. As Rane unlocks his cuffs, there is still no blood or bullet hole in the agent's seat. Later, when the plane is going down and the dead agents are leaning forward, the blood can be seen on the FBI agent's head and a bullet hole can be seen in his seat that wasn't there before.
When Cutter first enters the tent at the fairgrounds, the announcer can be heard talking into a microphone. When we see the announcer in the background, he is talking into the microphone but no voice is heard.
When Cutter is at the ticket counter before boarding the plane, a huge zit can be seen on the right side of his face. The zit disappears, reappears, and changes in size throughout the rest of the movie.
When Charles Rane is being led up the steps back to the plane in Louisiana, Vincent shoots the FBI agents. Charles Rane runs up the plane and makes it all the way up to the top step and past Mr. Forget. After we see Rane run back onto the plane, they cut to a wider shot which shows him running up the steps again - about 6 steps down from the plane and Mr. Forget.
When Ranes jumps out the window in the beginning of the movie, the customer sitting at the table he jumps on lands on top of Ranes when he hits the ground. The shot cuts away and when it cuts back Ranes is on top of the café customer, and he gets up and runs away.
The red Corvette convertible Cutter is shown driving changes model years when he pulls up to the hotel. This is most noticeable by looking at the car's parking/cornering lamps, which change from separate to combined units.
When Cutter disarms the terrorist near the bathroom and puts a gun to his head, terrorist Matthew is shown walking behind Rane, Marti and Ms. Ritchie as they arrive on the scene. But Matthew does not appear in the following stand-off, even though he was present moments earlier.
When Cutter rides away on the motorcycle, a shot of the plane shows the door closed and nobody else being released from the plane. A minute later when the FBI arrive at the airport, passengers are again being released from the plane. There is no reason why the terrorists would have closed the door and stopped releasing passengers, and then started over again.
While landed for refueling, Rane tells Chief Biggs to take a look at the plane door just forward of the landing gear. As the body of the pilot is thrown out, the reflection can be seen of the crew holding some sort of landing mat in the planes fuselage. You can then see the pilot land on the blue mat.
Early in the movie, just before the plane lands in Lake Lucille, Louisiana, there are two exterior shots of the plane. In the first, the plane is flying over Long Key, in the Florida Keys, then a few minutes later it is over the Upper Florida Keys, over 600 miles from Louisiana.
When FBI agents who escort Charles Rane aboard the aircraft display their credentials, you can clearly see the badge of a US Federal Marshal (silver star with circle) and not the gold shield of the FBI. In most cases, Federal Marshals are the ones who escort prisoners across the country, not the FBI.
During the lunch with the airline executive, Cutter mentions that El Al, the Israeli airline, is the only airline that has never been hijacked. This is untrue, most certainly at the time the movie takes place. The one (and currently only) hijacking of an El Al flight took place in 1968, and was resolved through negotiations without casualties.
Bathroom doors on planes have a spring that shuts the door. When Cutter leaves the bathroom to get the phone, the bathroom door is swinging loose on its hinges. This is shown when the terrorist turns around to see what was making a noise, and sees the door swinging loosely. Then when Cutter returns to the bathroom, he has to push the door to see out. He repeatedly pushes the door, and relaxes pressure allowing the door to close by itself. It even closes by itself when he leaves the bathroom. Now the door seems to have the spring hinge that was absent earlier.
Just as Cutter climbs onto the nose gear of the departing aircraft it is seen rotating for takeoff. The takeoff speed for this type of aircraft would be well in excess of the speed that the sheriff's car could achieve.
While chasing the plane in the Sheriff's car, Sly says to Cutter, "Hey John, you bring your ass back alive, do you hear me?" to which Cutter replies, "And miss the opportunity to get back at you? no way!", which makes no sense. This possibly indicates that Sly said something along the lines of "don't get yourself killed" in one of the takes and Cutters response to this was used in the final edit as this would make Cutters response more feasible.
In the last scene in the air, one of the aircraft doors is completely sucked out of the plane, though when the plane is landing all doors are still in perfect condition. The plane's left side faces the camera as it lands which shows both doors still in place. The door which was blown out is located on the other side. When Biggs stops to offer Cutter and Marti a ride into town, in the background you can see emergency workers using this door to board the plane.
When Cutter talks to Rane on the phone while the plane is descending, Cutter mentions "Vincent" the terrorist he had just fought with and had him tied-up. But Vincent never told Cutter his name and it has not been spoken by any other character, while the name-badge he is wearing only says "Robert". Therefore Vincent's name should be unknown to Cutter.
While Cutter is in the bathroom when the terrorists take control of the plane, the first thing Cutter hears from what is happening, is a terrorist yelling "sit down". Yet somehow he does not hear the previous sounds of the gun-shots or screaming passengers.
When the police break-up the fight between Cutter and Rane at the fair, Cutter tells them Vincent, one of Rane's men and wearing a tan jacket, is also on the fair grounds. But Cutter never saw or confronted Vincent at the fair and did not see him leave the plane. So how could Cutter know Vincent was at the fair and also wearing a tan jacket, given he was not wearing it when he last saw him?
When Cutter escapes the two police officers custody he steals a motorcycle and heads straight towards the fairground in pursuit of Rane. However, he never actually witnesses Rane or his men leaving the plane, so how does he instinctively know to pursue Rane at the fairground?
After Cutter throws the main terrorist out of the plane near the end of the movie it is clear that there is a green screen and a wire holding him up, because he falls out horizontally and does not fall out and towards the ground just out and horizontal.
When the aircraft lands at the airfield we are told by the control tower that the airfield does not accommodate aircraft of that size. When the plane lands we see airstairs approaching the plane to let passengers off. A small airfield which does not accommodate such aircraft would not have a set of airstairs.
Agent Henderson is shot in the arm during the gun fights when Rane runs back onto the plane. Shortly after when he talks to Cutter on the radio while the plane is returning to the airfield, and when he is seen on the runway after the plane lands, the sleeve of his shirt is still stained in blood, but his arm does not appear to be in any pain or discomfort and he does not even have it in a sling, despite just taking a bullet.
The goof item below may give away important plot points.
After having her first conversation with Cutter (Snipes), Marti is asked by one of the terrorists (Elizabeth Hurley) who she is having a problem with... after learning that there is a security expert on board, the terrorists do nothing with the information - they don't even watch Cutter to make sure he is seated before they start their takeover plan.