Factual error: When Mr. Hadden reviews Ellie's life history on his airplane, he says she graduated from MIT 'magna cum laude'. This is impossible, as MIT does not award academic honors to graduates.
Factual error: The geography around the VLA in New Mexico is actually relatively flat - in fact one of the reasons why the array complex is there is because the land is flat. The canyon in the film was actually Canyon de Chelly, in Arizona, more than 170 miles (270 km) away. But in the film, when Ellie goes to the canyon, the radio antennas seem to be right there, insinuating that the canyon is part of the VLA's magical desert scenery.
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.
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.
Factual error: When Foster is going to Japan, a Harrier jet transports her to a ship. The ship is underway, traveling at quite a clip according to the wake. The Harrier landed on its heliport platform, facing the stern. Harriers hover, but cannot fly backwards at more than a crawl. It would have crashed.
Factual error: The last time Eleanor Arroway talks to S.R. Haddon, he's aboard the Russian space station Mir, and Haddon explains that he's up there because the "low oxygen" and zero gravity counteracts his cancer. In fact, there is no "low oxygen" environment aboard space stations or other spacecraft. Low oxygen content would, of course, kill any astronauts or cosmonauts in short order. The breathable air in spacecraft always has at least the same oxygen content as Earth atmosphere at sea-level. In fact, most Russian missions used excessive amounts of oxygen. S.R. Haddon's original dialogue was probably "high oxygen and low gravity," but the line was bungled and allowed to remain in the film.
Factual error: The scene where Ellie and Palmer are looking at the stars next to the Arecibo observatory dish, they are looking at the constellation Cassiopeia. This constellation is visible to the North. However, judging from the parts of the antenna structure visible in the background, they are actually looking South. The suspended walkway/cable raceway connecting the control room and the antenna structure visible in this shot is on the North side of the dish. In real life, the control room and observation areas are on the North side of the dish. It is also not clear what time of the year this was but Cassiopeia is not visible from Puerto Rico during part of the year due to its low elevation above the horizon.
Factual error: Hokkaido island geography shows a relatively smooth coastline. The location of the second machine cannot be natural, but must have been added post production.