Character mistake: In the first scene inside the Prometheus, after she comes out of deep sleep, Vickers asks David for a robe, and asks "how long?" meaning how long have they been asleep. David, a robot, answers "2 years, 4 months, 18 days, 36 hours, 15 minutes." The actual statement from this highly precise robot character would have been "2 years, 4 months, 19 days, 12 hours, 15 minutes."
Revealing mistake: Each crew member has a monitor on their spacesuits that they use whenever they are exploring the caves. Whenever the monitor is shown, each crew member's individual heartbeat is shown in the lower left corner of the monitor. But no matter which heartbeat is shown, every time a heartbeat on the monitors shown, it is always the exact same heartbeat, despite the various changes in panic and stress throughout the movie.
Revealing mistake: When Fifeld and Millburn find the dead bodies, just after Millburn says "This thing opened up from the inside. Looks like it exploded", the shot cuts to Fifeld flashing his torch over the corpses. During this shot, a corpse's arm to the right of Fifeld is shown wobbling around.
Continuity mistake: After Elizabeth tells Janek the engineer is headed for Earth and it needs to be stopped, Vickers shouts to Janek, "Captain, let's go." Janek is then shown looking downwards with his lips clenched shut and his eyes are clenched a bit. In the next shot, his mouth is suddenly open and unclenched, looking straight forward with no time to do so.
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.
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.
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 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.
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.
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: 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.
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.