Vickers' dark roots in her hair appear, disappear and re-appear during the movie.
(at around 4 mins) When the sacrifice Engineer's arm breaks off, the remaining limb is just past the elbow, and can be seen as such when he falls into the river. When he's shown at the bottom, the point of loss is much closer to the wrist.
(at around 13 mins) When Meredith Vickers finishes her push-ups, just after 'waking up', she is wearing cloth around her chest. After the shot where she puts on her bathrobe, she wears no cloth under the robe.
(at around 1h 40 mins) Shaw is talking on her radio to Janek. Vickers is in the background and starts to get up from her chair, but in the next shot (a close-up of her) a moment later she is still in her chair, then gets up again.
(at around 58 mins) When Charlie and Elizabeth are discussing the DNA results, you can see Elizabeth from behind with her hand draped over her knee, but when it switches to her face, her hand is against her head.
(at around 38 mins) At one point the characters use "a carbon probe" to date a dead alien body. Carbon based dating of organic remains is based on knowing both the ratio of radioactive carbon isotopes over time in a planetary atmosphere, and the level of such carbon absorbed into the body of a living organism by it breathing. So far, we only know the atmospheric carbon ratio for one planet: Earth. Even with advanced technology, you'd always need to know the carbon sequence of the home planet of an alien species to carbon date anything from there. The movie's plot clearly shows that no one knows the origins of the Engineers. Logically then, the carbon probe sequence is impossible.
(at around 33 mins) When inside the structure, the research team determines the air is breathable inside the cave and despite orders from Vickers to not remove their helmets, all of them do so. Apart from possible hazardous toxicity in the air, another issue when investigating a different problem could be lifeforms, including microscopic ones such as viruses or bacteria (or an equivalent that could live on a planet). Even if the air is breathable, there is a risk of contracting a dangerous disease and bringing it back to Earth. As a biologist, Millburn should be the first to warn of such a risk. And even if a biologist were not on board, surely there are protocols and procedures that instruct the crews of ships about such matters.
(at around 47 mins) Ford and Shaw were extremely unprofessional with handling the Engineer head. As a discovery considered to be of utmost importance, they should have taken numerous tissue samples, carried out thorough chemical and biological analyses of the samples, and many, many more, careful step-by-step progress which would have taken several days, not just "power on and see what happens". They acted like curious kids instead of highly trained professionals.
(at around 45 mins) Even though there is a storm that discharges static outside the cave, the communication from the ship to Fifield and Millburn is excellent, both audio and video.
(at around 1h 6 mins) The buggy David is driving would not have fit through the small triangular opening of the pyramid which leads to the Engineer's U-ship.
(at around 23 mins) A CO2 concentration of 3% in the atmosphere is still not a lethal amount for human beings. Only after 5% does it become toxic. However, Ford actually states that the CO2 levels are *over* 3%, suggesting that was the minimum amount the preliminary sensors had detected.
Despite being set 30 years before the events of Alien (1979), the technology available to the crew on board the Prometheus seems to be far more advanced than anything seen in the 1979 movie. However, the Prometheus is a state-of-the-art science vessel, whereas the Nostromo is simply a cargo towing vehicle that does not require as much high-technology (it would be like comparing a fishing trawler to a nuclear submarine). By the time of Alien, the Nostromo is clearly an old ship. It could well have been made even before the Prometheus was.
(at around 1h 21 mins) In Miss Vickers' suite there is the MedPod. However the MedPod states it is configured for male use. A bit strange when there are so many females on board including the mission director. However, the med-pod was not there for the crew's use (Vickers told Shaw not to touch it) and was clearly there for Peter Weyland's use as he was already in failing health with little time left to live.
(at around 1h 13 mins) When David pulls down the holographic Earth in the alien ship control room, a closeup shows the present shape of Africa. How could they possibly know what Africa would look like after the breakup of Pangea billions of years ago? However, the Engineers had obviously been back to Earth more recently (within the last 2000 years) as they had already decided to eradicate humanity.
(at around 52 mins) When David is talking with Charlie in the bar/lounge, David has the drop of black liquid on his right index finger intending to place it in Charlie's drink. But during the lead time, his finger touches other objects such as the glass, bottle and the metal billiard ball. However, it is plain to see that David always keeps his right index finger extended throughout the scene and the tip of it (where the black liquid drop is) does not come into contact with the billiard ball, glass or the bottle. The first contact the tip of his finger makes is Charlie's drink.
(at around 30 mins) All EKG monitors of the expedition party's HUD show the same heartbeat pattern and rate regardless of individual or stress.
(at around 45 mins) When testing the alien head for possible contagious diseases, the tests can only check for known bacteria or viruses. That means that any contagion completely indigenous to that planet would remain undetected since it would not be known and therefore it would be impossible to know what to look for in order to detect it.
(at around 1h 55 mins) When Dr. Shaw is talking to David near the end of the movie, you can see wind blowing her hair inside the helmet, suggesting the helmet was added with CGI.
(at around 25 mins) Just before Dr. Holloway points out the area to land, he unstraps himself from his chair. While leaving the chair he bumps it and you can clearly see the chair is loose on the floor.
Even though there is no actual on/off button for a microphone on the suits, the audio from each character is either heard or not heard by the others, depending on what the situation calls for in the script. Also, while not wearing any earphones the characters can hear each other just the same with or without the helmets on.
When Shaw is fighting the Engineer at the end of the movie you can clearly see the rig that pulls her back through the air as she is "thrown" against the side of the cabin.
(at around 1h 10 mins) When Charlie gets sick on the second outing, Elizabeth calls to have "a medical team standing by" when they get back to the ship. The ship's medical team are all in the field with her.
(at around 18 mins) When Charlie is describing the civilizations that provided the clues and star maps leading them to the distant moon, he explains that these civilizations were all separated by centuries and had no contact. In this list he includes Sumerians, Babylonians, and Egyptians (among others). The Babylonian Empire rose out of the city-states of the Sumerians, borrowing heavily from their language, culture, and religions. It is also well known that the people of Sumer/Babylon had much contact with the ancient Egyptians via trade and war.
(at around 1h 45 mins) Near the end, Shaw and Vickers are racing away from the crashing spaceship and continue to run in the same direction it is approaching. While dramatic, these are two smart women - this is not a teen slasher movie - so they would know better and could have gotten out of the way by running 90 degrees to the side instead.
(at around 54 mins) It makes no sense for Janek to ask Millburn and Fifield where they are (after he was alerted by the computer regarding possible lifeforms), since the "pups" already mapped the caves and the rendered map was sent to the ship's computer and he can see that the location of each member displayed in real time (for example F and M, for Fifield and Millburn).
(at around 47 mins) The alien head is on the examination table. A probe is to be inserted into the head. One of the women says: "30 amps. No more." A current of 30 amps through any (Earthly) organic material would cook it. Thirty microamps in or near a brain would have been more appropriate.