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Near the end of the movie, when Louise has locked herself in the clean room, calling the Chinese General on the satellite phone, Agent Harper has his gun aimed at the window and tells her she is committing treason. Treason only applies with enemies of the U.S.. Although this is a fictional movie, there was no mention of the U.S. being at war with China.
Errors in geography
When a Pakistani soldier is seen on the monitor, his uniform's color and shape are not those used by any of the forces of Pakistan. The ribbons on his left chest and the badge on his right chest do not belong to any forces of Pakistan. However, his formation sign on his upper left arm looks like one used by the Joint Staff.
The scene were Louise Banks and Ian Donnelly arrive by helicopter shows a panoramic view of the alien landing sight and human camp. As the scene progresses we get a stunning picture from the air. The campsite has what looks like 4 large lighting trees with shadows from the morning/afternoon sun projecting onto the ground over twice the lighting trees length. The alien ship on the other hand as no shadow apparent. Even though there is mist/fog on the ground below it, there should be some form of shadow visible from such a large object with the sun at that low level.
Incorrectly regarded as goofs
Louise is told to translate some overheard Mandarin and is momentarily confused at hearing the Mandarin word for "suits" before realizing that it is a reference to Mahjong. In actual Mandarin, the word for "suit" that refers to clothing and the word for "suit" that refers to a classification of cards in a card game are not the same word. If the speakers had really been using the word "suit" in the card-game sense, Louise might have initially translated it as "flower-color" and been confused, but the only way she could have translated it initially as "suit" would be if she already knew of the card-game meaning. However, this is not a "Factual Mistake". There is no indication in the movie that Louise ever thought of "suit" in the clothing-sense. There are indeed suits (in the card-game sense) in Mahjong, but Mahjong is not a card game; it is played with tiles. In other words, Louise may have translated it as "suit" in the card-game meaning without realizing yet that the referenced game was Mahjong; and that (as well as the fact that neither card-games nor Mahjong are directly linked to the topic of the rest of the Mandarin conversation) may be where Louise's initial confusion arose from.
When Banks and Donnelly are arriving at the Montana site, they are shown traveling in a CH-47 Chinook, a tandem rotor helicopter. However, as they are circling for landing, the shadow of their helicopter only has one rotor. Actually, the CH-47 Chinook seen in those shots is a different helicopter landing at the base as the same time they are and seen from their point of view. The helicopter they are traveling in has one rotor.
The movie treats Top Secret security clearances properly at first by taking away Ian's and Louis' phones, but the rest of the staff would also be under such restrictions. There is no way that Captain Conspiracy would have had access to a laptop with WiFi, let alone be allowed to access the sites he was shown to be watching.