Several shots early in the movie where the crew are at their stations the monitor images are projected onto their faces. This is impossible - they would have to look into projectors instead of monitors, so this effect just doesn't make sense.
When Ripley visits Parker and Brett to inspect their progress, she says "Yeah, you'll get whatever's coming to you." But the word "Yeah" is missing entirely from the soundtrack, and the rest of the sentence is out of sync with the video. This error is not present on the original Alien DVD box set, where Ripley's "Yeah" is muffled but quite audible. But the 2003 theatrical release and the new "Alien Quadrilogy" boxed set both have the word entirely absent.
When the crew is sharing a meal after Kane regains consciousness, Parker is shown to be talking. The shot changes to show the crew from a closer angle, and although we can still hear Parker speaking, he is shown to be laughing softly and not speaking at all.
During the landing sequence, Kane issues the instruction "Roll 92 degrees port yaw." Roll and yaw are two separate directional axes. The correct instruction (and what the ship actually does) is "Roll 90 degrees port."
At the very beginning, when Dallas is going through the computer login sequence to communicate with Mother, and all the green-lettered commands are flashing by, the word "ALIGNMENT" is spelled "ALLIGNMENT".
During Ripley's final log entry, she identifies herself as the "3rd officer." She is technically the 3rd in command, or "2nd officer." (Dallas is Captain, Cain is the 1st officer, Ripley is the 2nd officer).
When Kane, Dallas, and Lambert are in their spacesuits exploring the alien ship, all are wearing white/gray fabric covers on their heads under the domes of their helmets. These are like the "communication carriers" or "Snoopy hats" worn by Apollo and later astronauts. But when Kane's helmet is cut off in the sick bay, no Snoopy hat.
During the "chestburster" scene, Parker is holding Kane's arm when he is convulsing. However, after the alien arrives and Parker has clearly backed away with arms in the air, you can still see Parker holding Kane's arm.
During Parker's fight with Ash, the sleeve on his right shoulder suddenly becomes torn and a safety pin is visible holding it together. In the next shot we see his shirt intact and we see Ash tearing it.
When Ripley comes out of the closet with her spacesuit on in the shuttle to try and get rid of the Alien and she straps herself into the seat the straps are up over her shoulders. Then she scene switches to her fingers pushing the switches and the scene then goes back to her in the seat and the straps are down on her arms. The next time the scene changes again the straps are up over her shoulders.
When Ripley consults Mother, she puts her left hand on a ledge and begins to type with her right. In the close-up she is typing with both hands, but when we cut back to the wider shot, she is still leaning on the ledge with her left.
When Lambert comes to tell the rest of the crew that it will be ten more months until they reach Earth, Ripley is leaning forward listening to her. In the next shot she is leaning against the wall when she says, "Oh God."
When Ash wrestles Parker to the deck, Lambert can be seen dragging Ripley through a hatchway into an adjoining corridor. In the next scene, Lambert is just picking Ripley up. She moves Ripley only a short distance toward the hatch before dropping her to assist Parker.
When Ripley finds out the truth from Mother, Ash is seen standing next to her. A brief scuffle ensues and Ripley leaves the room. As she leaves there is no injury to her but when the door opens on the other side she has a bloody right nostril.
When Dallas is first entering Mother, as he passes through the last doorway... when he is seen outside the door, one of the lights on the door-frame is burned out (on his left) but in the next shot, it is lit.
During the chest-burster scene just before Lambert is sprayed with blood there is a quick shot of alien bursting out of Kane: on a freeze-frame a hole is clearly seen in the table right under Kane's raised hand.
The planetoid where the Nostromo finds the alien spaceship is said to be 1200 kilometers diameter with a surface gravity of .86G. (Earth is 1G.) The horizon would curve visibly on a moon that tiny. By Newton's Law of Gravitation, a body that small would need a density of 50 grams per cubic centimeter to achieve .86G. This is more than twice the density of osmium, the densest element known. It's unlikely that the moon would be made of a massive ball of some hitherto unheard-of, super-dense, stable element. Together, this indicates that the size of the moon is incorrect.
When the Nostromo approaches the planet, there is too short time between the phases of the approach - such distances in space would require either much more time or much greater speed. In the latter case the deceleration required for orbital insertion would have a lethal effect on the crew.
A moving dippy bird toy is show in the opening scene. Dippy birds require water to work. As the crew is in hibernation and has been for some time, the water in the glass in front of the dippy bird would have long ago evaporated, so the toy would be motionless, not dipping.
Dallas informs the crew that Mother, the ship's computer, has interrupted their journey having intercepted a transmission of unknown origin, an acoustical beacon that repeats at intervals of 12 seconds. Acoustics is a branch of science dealing with sound. Sound is a mechanical wave that requires a medium, like air or water, in order to propagate. There is none of that in space. The tagline of the movie, "In space no one can hear you scream" also applies to an acoustical beacon.
A close-up of the Alien egg when Kane is looking at it shows water droplets falling upwards off the egg, revealing that the shot was done with the camera upside down. (according to Trivia, this is an intended effect by Ridley Scott)
After Lambert hits Ash with the electric prod, the camera pans down and we can see wires on the ground leading to the prop Ash torso atop Parker. The torso has no legs, ending at the waist. (Visible in 1979 theatrical wide-screen and full-screen versions, but not in 2003 director's version).
When Parker and Brett are walking through a long hallway and complaining that none of the other crew "come down here", their reflection can briefly be seen in a mirror behind them. Mirrors were used to make the set hallways look much longer than they actually were.
When Dallas, Kane and Lambert are inside the alien ship containing the space jockey, there is light coming from the left side of the screen, despite them being inside an internal chamber of the derelict spacecraft.
The goof items below may give away important plot points.
Just after the time limit to override the self-destruction of the ship has expired, the clock starts counting down from 5 minutes to 0. We see the clock counting down and it cuts away when the timer reaches 4:57, and then mother says "ship will self-destruct in T-minus 5 minutes."
Mother's reports of the remaining time in the countdown to self-destruct all say that the explosion will occur "in T minus minutes". In fact, as she is saying that the event will occur after a certain period, the "T minus" is unnecessary. She should simply say that the event will take place "in minutes".
As Ripley blows the alien out of one of the Narcissus' aft nozzles, the engine exhaust is obviously water because it dribbles down the camera. Ridley Scott stated that they used water as a substitute for some sort of plasma. At any rate, there's no reason for the exhaust - whatever it is - to dribble down a camera glass that isn't supposed to be there.
In the split second shot where the alien drives its tongue into Parker's head, you can see he is bald, but throughout the rest of the movie, he has hair. Also, in a freeze-frame of the shot you can see the alien tongue is white, not airbrushed like the rest of the creature.
Jones vanishes from his carrier as Ripley boards the Narcissus. This is deliberate because the fiery explosion effects in the scene would be traumatic for the trapped animal. However, as a consequence, Sigourney Weaver handles the carrier more roughly than Ripley would if Jones was inside.