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.
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.
During Elizabeth's auto-surgery, you can see that a fake body is inserted during specific elements, such as when the laser opens the abdomen. You can tell by the fact that her legs visible are shaking when there is a real person and still when not. (the laser element of the scene was done with CGI)
About 103 minutes (1:43), 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. This is clearly an editing error.
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.
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 or would have been more appropriate.
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, 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.
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.
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.
In the first shot of Prometheus, it is moving at high speed through space. When it enters the target planet/moon's atmosphere, it must slow down which should mean that the thrusters would be pointing forwards and down, not straight backwards as seen. However, the ship will have slowed down (offscreen) as it approached the destination moon, though it would still be necessary to have the thrusters pointing backwards so as to propel the ship to a landing site. It does not mean the ship was still travelling at the same immense speed it did when in deep space. Also, the thrusters are indeed pointing downwards when the ship lands.
The paintings found in the cave on the Scottish Isle of Skye are said to date back 35,000 years or more, according to Shaw. The northern part of the British Isles was covered with the icecap of the Würm glaciation at that time. However, Cro-Magnons (the first early modern humans) are believed to have been present in the regions of what would become the British Isles around that time, and depopulation of the region did not occur until around 23,000 years ago.
Meredith Vickers mentions that she flew herself "half a billion miles from ... Earth." 500 million miles, however, is only about Jupiter's aphelion; interstellar distances are conveniently expressed in light-years or parsecs, and if one were to (ab)use miles or km, it would be trillions, at least. However, it is quite obvious Vickers was being sarcastic and speaking figuratively when she made this comment to Janek.
When Elizabeth has the alien "fetus" removed by using the "Pauling Med-Pod", she breaks the umbilical cord which is still internal, thereby leaving the "placenta" in her abdomen. This alone would probably kill her, causing her internal bleeding. However, as this was not a "traditional fetus" (as David described it), it is questionable as to whether a traditional placenta had even formed. Even if there was a placenta of some kind, it is still possible for women to have a "retained placenta" even after a C-section which can later be expelled from the body naturally or with the assistance of medication.
Just before the crew descend into the lower level of the alien structure, a white folding chair can be seen leaning against the wall behind them. However, this was equipment brought in by Milburn. You can see him carrying it when he emerges from the personnel carrier vehicle when the team first arrive at the structure.
Near the end of the movie Shaw enters the lifeboat and she is carrying an axe. When the Engineer enters and attacks her the axe is gone. However, you can clearly see the axe in Shaw's right hand as the Engineer enters the pod and confronts her (Shaw's back is to the camera). Shaw then drops the axe as the Engineer lunges towards her. You can even hear it hitting the floor.
David is an android and, therefore, does not require sustenance. While taking linguist lessons and before the humans exit stasis, he is eating and drinking. However, there are various possible reasons why David is eating and drinking. It could be because he wants to experience food and drink to become more human (androids in the previous Alien films were seen eating and/or drinking). It is also likely that androids, like any machine, require fuel of some sort. Food is simply a biological form of fuel.
While watching "Lawrence of Arabia," David has white treatment in his hair. A few seconds later, his hair is clear of the treatment. After another few second the treatment is in hair. However, this sequence shows how David spent two years by himself aboard the ship while the rest of the crew were in cryosleep. The sequence is not necessarily linear, though it could also show David repeating certain activities several times during that two year period (in order to lighten hair, multiple treatments are often required).
Holloway regards the mission as a failure because the Engineers on the planet are all dead. This, however, makes little sense, as it's obviously very unlikely that this was the Engineers' home world. Additionally, his work has directly found conclusive proof of the existence of advanced intelligent alien life, found preserved biological specimens of that life to examine, and working advanced technological artifacts from their culture including writing, art and still-working information technology. The mission had been a massive success by any metric.
That said, Holloway could be considering it a failure in that he wanted to meet the Engineers and interact/ learn from them directly.
The windscreen of the personnel carriers they use on the planet has the familiar arc pattern created by the wipers. However the carriers have been been kept in the hold the entire journey and would have no dust on them whatsoever. Plus the wipers are never seen being used so they could not have created them. However, that does not mean the carriers had not been used on a previous mission or even exposed to weather as they were being loaded into the Prometheus.
Near the start when Charlie is summoned to see Dr Shaw's cave writing discovery, he has a bright orange coat on. When he enters the cave he has a dark gray/green coat on. However, before Charlie runs towards the cave we can see he is wearing two coats, the bright orange one on top and the darker coat underneath it (along with a zipped up bodywarmer underneath that). Presumably it was cold outside, but he took the orange coat off by the time he reached the cave.
The goof items below may give away important plot points.
When Vickers is standing and facing Weyland while she talks to him about why he made the journey, her hands change position several times. In one shot, they are in front of her while in the next shot, they are behind her.
Prometheus crashing into the Engineer's ship would have pushed both vessels AWAY from where the Engineer's vessel finally crashed. When two objects strike one another, especially when one is being propelled as was the Prometheus, the impact drives both objects in the direction the propelled object was going, even if only slightly. The Engineer's ship should have fallen to the immediate left of where Vickers was standing on the surface at the very least, if not several miles away.