Factual error: In the zoom-out at the very beginning, we hear broadcasts going back in time as we zoom out through the solar system. However, we hear broadcasts going back through time roughly 40 years. Shouldn't we be 40 lightyears out from Earth to hear them, rather than just in the Oort Cloud beyond Pluto? Radio waves travel at the speed of light like any electromagnetic wave. EM waves should not be confused with sound waves, which move much slower than the speed of light.
Factual error: At the end, after Ellie testifies before Congress, she departs the Capitol building to a waiting limo. The media is there waiting for her. Behind the reporters appears to be the Reflecting Pool, and the Washington Monument at the far end of it. However, in reality, the Reflecting Pool is actually located between the Lincoln Memorial and the Washington Monument, not the Capitol. While there are two Reflecting Pools, the columns in the movie are the columns of the Lincoln Memorial, not the Capitol. Furthermore, the steps leading to a street in front of the reflecting pool are located at the Lincoln Memorial; the Capitol has a large green lawn between it and the street.
Revealing mistake: When Ellie is traveling through space, she unbuckles herself from the chair to retrieve the compass. The chair then breaks off from the violent movements of the space pod, and slams up against the ceiling. At this moment, Ellie is in deep space in a completely weightless environment. She is floating, suspended in the pod and the chair itself floats a bit before being slammed upwards by the force of the pod movement. But, some small parts of the chair (bolts, etc.) are seen falling directly down, towards us in obvious full gravity; revealing that the scene was actually shot in normal gravity.
Continuity mistake: When the Machine is used for the second time (with Ellie in the pod) the large outer ring is set spinning. This brings the total number of spinning rings to three. However, when video of the pod falling through the machine is played back on the TV screen, the outer ring is fixed horizontally and not moving at all. Only the two inner rings are spinning.
Continuity mistake: When Ellie arrives back from her travels, the capsule lands in a net supported from four pillars, and to decellerate effectively, both the net and capsule end up in the water. However, when we view the splashdown from a CCTV camera (Cam 03) when Ellie is in quarantine, neither the net nor the pillars are to be seen. (02:01:40 - 02:03:15)
Factual error: A big deal is made of the fact that no camera can be installed in the pod because of the high local magnetic field. This is idiotic. First, it is easy to shield a video camera from an electromagnetic field. Bog standard technology. Second, Super 8 film cameras could easily be used - they have no electronic parts worth worrying about and they're small enough to have multiple units installed - and if the electromagnetic field is strong enough to fog film, it is strong enough to kill any human being knocking about the place.
Continuity mistake: When Ellie drives back to the observatory after hearing the first audio transmission from space, there are several shots of her holding the steering wheel with her left hand while giving instructions to the other men. In one shot you see that the wrist-watch is turned upside down: the watch face is on the inside of the arm. In the following shot of her in the car the watch face is on the outside of the arm.
Continuity mistake: When Ellie is in the pod and is talking to Kent, her monitor has the word "Hadden" in the top left hand corner. In subsequent shots, there is no "Hadden" on the monitor.
Continuity mistake: During the scene in which Ellie is preparing to go in the pod through the alien machine built in Japan, she puts a small digital video camera on the side of her head (with a headphones-type headband holding it in place). During subsequent shots of her in the pod before it drops (and there are many from different angles), the camera's orientation changes noticeably from shot to shot.
Plot hole: During the Congressional hearing, it is suggested that the alien signal could have been faked from a satellite - as Ellie only has her own experience to go on, it leaves her believing what happened, but still with an element of doubt. However, as a professional astronomer, Ellie would have immediately dismissed this since a simple parallax (triangulation) would have confirmed that source was at the distance of Vega - a distance far too great for any rocket to reach. (This is mentioned in the book). In fact, this is mentioned early in the film, when the employees in New Mexico calculate the source of the signal while it is transmitting prime numbers.
Visible crew/equipment: During the scene when Ellie has discovered the Signal, and is in the control room with the guys, she turns to one of them and says "Make me a liar". Right when she turns, you can see some bright, smaller, roundish white lights reflected in her eyeglass lens. These are probably camera lights, as their appearance wouldn't match the computer screens or natural lighting in the room.
Continuity mistake: When they realize the signal's counting prime numbers, watch the man in the red shirt behind Ellie when 11's being counted off. He's counting on his fingers, fills up his right hand, and moves to his left. The angle then changes to a closer shot, and his left hand is now curled up, with no numbers counted off on it at all, and he continues on his right.Jon Sandys
Continuity mistake: Ellie tells Palmer her father died when she was nine years old. Later, when Mr. Hadden goes over her life history to impress her, the dates of her birth and her father's death indicate she was ten years old when he died.