Revealing mistake: When Shaw goes to the med pod for her emergency surgery, as she quickly taps on the entrance door to the med-pod room, on the left-hand side of the frame you can see the door is already partially open and then opens before Shaw has finished typing in the code.
Continuity mistake: When the Prometheus collides with the departing spaceship, the close up of the impact shows devastating damage which results in a massive explosion and fireball as seen from the ground. However as the spaceship falls to earth there is no sign of any damage from the collision or explosion in the area where the Prometheus hit the ship.
Continuity mistake: During the final scenes, after the ships have collided and crashed to the surface, Elizabeth finds David's detached head inside the alien ship. She then takes the head with her to a ledge where she is about to lower David's body to the ground. In both places, David's hair keeps changing between shots: messy/neat/very messy, with no logic whatsoever.
Other mistake: In the scene with the crashed escape pod, everything inside is upended with books and stuff strewn everywhere. Yet there is a bottle of Vodka sitting perfectly upright on the bar in the background.
Continuity mistake: The alien's spaceship falls from the sky and crash in the ground with its bottom facing one side. It rolls to Meredith Vickers and Elizabeth Shaw. But it faces the other side after crushing Vickers.
Continuity mistake: When Vickers enters Peter Weyland's room to speak to him just before he embarks to see the engineer, her hands are clasped behind her. They remain that way in each shot where she is seen from behind. But every time the camera angle changes and we see Vickers from the front, her hands are suddenly clasped in front of her. This switching occurs repeatedly throughout the scene.
Continuity mistake: Prometheus is flown into the alien spacecraft, presumably to disable it from flying. However, after the alien craft has crashed and rolled over Meredith Vickers, the ship is facing face down on the planet, giving us a full shot of the back of the ship. There is no damage to the back of the bulkhead whatsoever, even after the bright explosion in the atmosphere.
Factual error: At the start of the film, the alien drinks some substance and starts to disintegrate into the water. You can see his DNA (double helix formation) floating in the water. This is impossible because DNA is in molecular level. You should only see his DNA floating amongst H2O molecules. Moreover - the alien substance appear to melt the DNA into black strands- impossible for similar reasons of molecular level of the structure.
Factual error: In the scene in the ship where Charlie exhibits the ancient artifacts that depicts the solar 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.
Continuity mistake: When Shaw is on the planet surface towards the end of the film, she isn't wearing any gloves. Later on, she suddenly has gloves again.
Character mistake: The ship travels approximately 35 light years, yet Vickers (Charlize Theron) comments they are half a billion miles from Earth. That would barely get them past Jupiter, much less another solar system.