Factual error: The type of surgery shown made by the machine transversely cuts the rectus abdominis muscles. Besides not being a standard surgical incision in order to "remove a foreign body" as stated, it seriously damages important muscles of the abdominal wall making any immediate active mobilization of the trunk virtually impossible, even under strong analgesia.
Factual error: Carbon dating cannot be used without knowing the amount of C14 in the atmosphere and its evolution in history. Using this method just after arriving at an alien planet is impossible.
Factual error: In the scene in the ship where Charlie exhibits the ancient artifacts that depicts the planetary system they are traveling to, he shows an artifact from Sumer, Babylonia, and Mesopotamia, and refers to these as "unconnected" cultures. In fact, the terms Sumer and Babylonia both refer to ancient Iraq, also known as Mesopotamia. The terms Sumerian and Babylonian are generally used to refer to different time periods in Mesopotamian history. These three terms refer to the same culture, and are not at all unconnected as Charlie said.
Factual error: As the ship lands the ship's voice states "temperature at 2.725 K." At that temperature, only helium would be a gas. All others would be frozen solid, thus probably no atmosphere. In a virtual vacuum. It would be virtually impossible for a breathable atmosphere to be present within the structure. This temperature is incompatible with life.
Factual error: In the scene showing the two left-behind crewmen as they discover the snake-like alien, one of them reports to the ship that the creature is "30-40 inches long." The scientific community worldwide has been using the metric system for decades and it would seem highly unlikely a trained member of a starship crew would revert to such an ancient system of measurement.
Factual error: In the beginning of the film strands of DNA from the engineer are shown degrading completely and then randomly reforming. That way would be impossible to get similar strands of DNA which are implied in the film to be in our cells. Only through replication is a DNA strand able to divide into two similar ones.
Factual error: When Shaw sacrifices the engineer to the alien she rolls out of the escape pod and lands with her hand and Holloway's ring showing. If the atmosphere was that toxic she would be dead and the suit would not be able to hold air pressure,.