During the first test of the space travel device, in one shot you can see all three rings on the device starting to move and spin. In the very next scene which is a wide shot, you can clearly see that none of the device rings are moving, yet they are supposed to be.
During the close-up of Fish watching Palmer's Larry King interview, the TV screen is reflected in Fish's glasses. In that reflected image Mr. King is talking, but the audio from the TV is Palmer's voice.
Ellie says, "There are over four hundred billion stars out there, just in our galaxy alone. If just one in a million of those have planets, and if just one of a million of those have life, and if just one in a million of those have intelligent life, there would be literally millions of civilizations out there." The math doesn't work. 400,000,000,000 times (1/1000000) times (1/1000000) times (1/1000000) is far less than one. The movie's creators were informed of this issue after the scene was shot and couldn't find a cost effective way of fixing the problem, so they left it in.
When the alien signal is heard for the first time, they state that the star Vega is about to set. Yet outside the window the radio telescope array is clearly still pointing up at the sky, when it should be pointing to the horizon.
Ellie says to Palmer that her father died when she was 9. Yet later in the movie Mr. Hadden set her birth date to August 25th 1964, and her father's death to November 10th 1974, so she was 10 at the moment of his death.
When Dr. Arroway first hears the alien signal at the VLA, she shouts into her walkie-talkie the Right Ascension and Declination that the signal is emanating from. Twice, she says, "Declination plus 36 degrees," but when she repeats it the third time, she accidentally says "Declination 36 hours."
Kent translates Adolf Hitler's opening speech wrongly as: "I declare the games of Berlin on the occasion of the FIRST Olympic Games..." However, what Hitler really - and correctly, too - says is: "...the ELEVENTH Olympic Games...". The German word for "first" is "erste," and for "eleventh" it's "elfte".
In the VLA control room when the message is first received, the Tektronix 420 oscilloscope is in the "Trigger - Edge Source" mode when Ellie decreases the vertical scale. When the message momentarily stops, she glances back at the same scope and it is in the "Display - Style" mode.
When Ellie is leaving Arecibo Palmer Joss leaves her a note. When we first see the note it is pinned to a wall. When Ellie looks at in on the wall the 9 in the phone number has a straight tail. She takes it off the wall and puts it down beside the phone. At that point it's a different note. The signature is different and the 9 in the phone number has a short hook, like a lower case g. In the next scene, when Ellie is packed up and about to get in the jeep to leave, she goes back in to see if she missed anything. She sees the note by the phone. This time it's back to the original note.
When the VLA scientists receive the video transmission, the "zoom" slider on the computer screen is on 0. Moments later, when they are asked to zoom out on the video, the slider is on 4, and the scientists move it to 0.
When the pods drop through the machine commences, the ship containing the control staff rocks severely (causing some of the control staff members to shout in panic as they lose their balance), and the machine itself is releasing brilliant light and a thunderous roar as the rings whirl like helicopter blades. Three or four seconds later, when the pod splashes into the catch net, there is little ambient noise. In the ship, staff members are suddenly sure-footed and tranquil.
Before Ellie first encounters the signal from Vega she is shown sitting on a cliff wearing beige jeans. A few scenes later when she is shown running back into the observatory she is now wearing blue jeans.
When Ellie calls in to Fish and Willie to alert them about the signal, the part of the room where they are sitting is dim, with no overhead lights on. Two seconds later (after we see Fish spring from his chair to use a PC in another part of the room), the overhead lights above Willie are suddenly on.
When the first test of the machine commences at Cape Canaveral, it is late afternoon, as indicated by the sunlight shining on the western side of the machine. However when the P.O.V. shifts to the spectators along the Banana River causeway, the sun in shining on the southeastern side of the machine, indicating mid-morning.
As Ellie steps down the stairs of the U.S. Capitol after testifying, the limousines drive away on a road that is on the west side of the U.S. Capitol. In fact, there is no road there at all, only steps that lead down to a small reflecting pool. This road was added via CGI.
The opening sequence contain impossible physics with the four planets (Earth, Mars, Jupiter and Saturn) that appear completely desynchronized as the sequence zooms out. The Great Red Spot on the gas planet Jupiter appear larger and centered near the equator rather than slightly positioned at the middle lower line of the planet.
A satellite image of Earth is shown when Ellie first receives the alien signal in the evening, however, the satellite image suggest morning in New Mexico as the sun is centered off the U.S. east coast.
After young Ellie's contact with the man in Florida on her shortwave set, her father praises her for the most distant contact to date, "One thousand one hundred and sixteen miles." The air distance from Madison to Pensacola is actually 906 miles.
The mountainous peninsula and bay on the east coast of Hokkaido, concealing the second machine, does not exist. At the actual location (midway between Shibetsu and Rausu) is a simple bulge in the shoreline, consisting of rolling foothills and farmland.
Every scene outside supposedly NASA facilities repeatedly mentioned as being in Florida show the California state flag flying below the US Flag. The official state flag of Florida contains a red-bar cross with the Florida state seal in the middle. The state flag of California shows a bear in the middle with a red bar at the bottom. The two flags could not be more different. The Florida state flag should be flying in those scenes, not California.
The opening sequence shows Earth, particularly the Gulf of Mexico, shows an incorrect shoreline. There is an indentation north of Tampa Bay that doesn't exist, as well as a very irregular Florida Panhandle shoreline.
The suggestion that a man-made Earth-orbiting satellite could have been used to simulate a signal emanating from a star is absurd. A satellite within Earth's or the Sun's gravitational fields can not carry enough fuel to maintain a position in front of a distant star for more than a fraction of a second out of every several hours. And since the signal was tracked from several locations on Earth, the sky would have to be filled with hoax satellites to fool more than one listening station. Moreover, the VLA alone would be able to confirm the distance of the signal from parallax.
The VLA in New Mexico does not listen for radio transmissions, but in fact takes radio "photographs" of space. In their Visitor Center they acknowledge the filming of Contact but debunk the premise of the film that their dishes could be utilized for the purpose described.
When Ellie first hears the signal from space, she calls back to the guys with a walkie-talkie and they answer her as well. But, when the guys press the talk button, her conversation doesn't stop emanating from the radio. Which of course it would.
The radio and TV signals that are said to have reached the star Vega could not. By SETI's own calculations, these signals are imperceptible from noise within 2 light-years; Vega is 25.7 light-years away.
In the opening galactic pullback scene, the oldies in the soundtrack are out of sync with the indicated distance from Earth. It takes only 4 hours for a radio transmission to travel from Earth to the edge of our solar system, yet 1960s music and news cues are heard as the "virtual camera" passes Jupiter.
In the first scene when Ellie is sitting outside near the VLA, the license plates on her car show a New Mexico tag on the front bumper. The state of New Mexico does not provide front license plates for vehicles registered in that state.
Joss implies to Dr. Arroway that he's not familiar with Occam's Razor (which, as a divinity student, he should be), but this is his style of joking banter, and he never flat-out says he's not familiar with it.
When Ellie receives the call from Mir, the Cosmonaut addresses her as "Comrade Arroway", a form of address that became outdated with the collapse of the Soviet Union. However, it is still commonly used out of tradition and habit.
When giving testimony at the inquiry, Ellie states that the travel lasted 18 hours for her and just a second for the witnesses. She had no way of knowing the exact duration of her experience since she didn't have a watch and any scientist who admitted being subject to a vivid illusion would know that subjective time is hard to reckon. Besides, the duration of the static recording was unknown to her and the public.
When the signal is transmitting the prime numbers, we are able to hear and count the transmission to number eleven. However, after that, when the actors stop counting and start talking at once with each other, the signal never pauses after what would be the next prime number, thirteen. Later it is revealed that the signal transmitted all the prime numbers to 101.
After Ellie notices the compass is floating smoothly, she unstraps from the chair inside the "IPV" and floats as well. Soon, the chair shakes violently loose from its anchor point, then slams into one side of the pod. When Mission Control resumes video contact with her, she's lying on the floor of the IPV, her cheek bloodied, but it's hard to tell if the chair is still mounted or not. The condition/position of the chair would confirm or refute her story of having traveled, rather than dropping straight through the spinning rings.
After a Control crew member gasps, "My God," there is a wide shot of the Control room staff and spectators as they gape in awe at the suddenly incandescent machine. However, the directions of the actors' gazes are inconsistent, with some of them facing far to the right of the machine's pictured location.
When Young Ellie runs to the bathroom to get medicine for her father, at the moment when we see her through the reflection of the pharmacy cabinet mirror reaching to open it, the red sleeve under her dark blue coat doesn't show in the mirror where instead we see a black sleeve.
The goof items below may give away important plot points.
Errors in geography
At the end of the movie, Ellie is sitting on the ground at the VLA radio telescope facility. She's sitting on the lip of a steep wash or small canyon, with the radio dishes of the VLA visible in the background. There is no such wash or canyon on the grounds of the VLA in New Mexico. The small canyon was filmed at another location and digitally added to the VLA grounds.
At the end of the movie, it is revealed that Ellie's video recorder recorded 18 hours of static, suggesting she really did go somewhere. It is peculiar that scientists in the movie neglected to include a simple clock in Ellie's equipment. Surely they would have wanted to see if time inside the pod would slow down since that is what the theory of relativity says would happen when you travel very fast (relatively close to the speed of light). Although in the movie the opposite occurs (time moves faster for Ellie) that clock would nevertheless have shown that 18 hours had passed inside the pod, while from the outside it seemed to pass straight through the machine, adding credibility to Ellie's story.
For no discernible reason, the tech that is holding Joseph's thumb back from the detonator pulls his hand back and after a moment gingerly places it on Joseph's forearm, allowing him to detonate the bomb.