Continuity mistake: Walter near the beginning of the film, is going over the ship's systems. He checks the fetuses inside a compartment and sees a dead one. As he removes it, the slot it came from is full of blood. He places it inside a container. Then as he hits the button to close the compartment, the slot has no blood in the next shot, and no implying he cleaned or decontaminated the slot.
Plot hole: The computer on board the ship mistakes David for Walter. This makes no sense as while a human being could be fooled by his appearance or his voice, a computer with detailed sensors and possessing the exact details of David's composition would not be fooled simply because the two "look" and "sound" alike. In fact, Walter, being a newer and more advanced model, should be composed of different chemicals and materials than the earlier manufactured David making it even less likely that the ship's computer would have mistaken the two.
Trivia: When David is cutting his hair, he is singing, "The Man Who Broke the Bank at Monte Carlo." This is a reference to the film, "Lawrence of Arabia." In Alien: Prometheus, David had a fondness for that particular movie and emulated Peter O'Toole, who played T.E. Lawrence. In the movie, Lawrence sang that song while riding on a camel in the desert.