(at around 8 mins) 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.
(at around 55 mins) 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.
(at around 22 mins) 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.
(at around 37 mins) When the rest of the crew is watching Dallas and Ash try to get the facehugger off of Kane, Parker asks, "How come they don't freeze him?" but his lips don't move when we hear this.
(at around 9 mins) 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".
(at around 14 mins) 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 around 1h 50 mins) 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, Kane is the 1st officer, Ripley is the 2nd officer).
During her final transmission Ripley identifies herself as "3rd officer." While she was originally third in command behind Commanding Officer Dallas and First Officer Kane, the deaths of those two placed her in command. She should have more accurately identified herself as "acting Captain" or "Commanding Officer pro tem."
(at around 1h 20 mins) 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.
(at around 56 mins) 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.
(at around 1h 40 mins) Just before Ripley enters the Narcissus (shuttle), she is carrying Jonesy's carrier with the "window" to the front. The next shot shows her holding the carrier with the window to the rear.
(at around 20 mins) When the members of the Nostromo are exiting the ship to leave to explore the Alien ship,the wind is blowing at high speeds, yet when the steam is shown from the lift it is just drifting down rather than being blown away at high speed. other scenes show the high wind blowing.
(at around 1h 19 mins) 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.
(at around 1h 50 mins) 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.
(at around 53 mins) 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 the first computer screen awakens, and when Ripley calls for a location check, we see/hear that the NOSTROMO has a registration number of 180924609; a second view of a new page on the screen AND in some shots outside the ship show the reg ID as 180286.
After the Nostromo has escaped from the planetoid and the crew gather in the mess area, the Weyland logo above the left-hand breast pocket of Dallas's shirt is gold colored. In the next scene in the medical center revealing Kane's recovery, the Weyland logo is now blue. It reverts back to gold in the subsequent chest-burster scene.
(at around 3 mins) A moving dippy bird toy is shown 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.
(at around 13 mins) 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. (Visible in 2003 director's version, but not in 1979 theatrical version)
(at around 1h 50 mins) Because she's no longer in a flight seat or in any way strapped in, when Ripley fires the shuttle's engines, the g-thrust should throw her against the aft bulkhead, but it doesn't.
In the takeoff sequence the "entering orbit" announcement is heard just after emerging from the clouds - this is impossible because the atmosphere ends at a much higher altitude than the top of clouds/dust layers, and the orbital speed cannot be reached in air even above a small planetoid, moreover, there must be a horizontal acceleration stage out of the atmosphere to gain the speed necessary for the orbital insertion.
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 lethal effect on the crew.
Just before the alien kills Brett - there is a close up of the alien with dry ice smoke blowing at the aliens head. This is a reused shot from later in the film when the alien kills Parker. The dry ice smoke comes from a pipe the alien broke when it attacked Parker. There should be no dry ice smoke present in the landing leg bay where the alien kills Brett.
(at around 11 mins) 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. However, it is obvious Dallas was referring to the signal being one that was audio only rather than one containing video.
(at around 33 mins) 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)
(at around 1h 50 mins) In final scene when Ripley uses the grappling hook on the alien. It shouldn't have been able to retract back up because its acidic blood should have melted it away. Unless, of course, the acid was frozen in the freezing vacuum of space (which it was exposed to).
As the remaining crew members are preparing to leave the Nostromo, Parker and Lambert are trying to deliver additional coolant for the air support system to the escape shuttle. One would expect a real spacecraft's escape vehicle already be stocked with such items and other emergency supplies. However it is made clear that the shuttle is not designed to carry so many passengers for long trips (only two cryotubes are seen inside it, suggesting it can only support two people for a long journey). It is therefore plausible that the crew would need additional supplies in order to survive.
The ship's computer, "Mother", deciphers the signal from the derelict ship and determines it to be a warning. Accepting that the crew was deliberately put into the path of the beacon by Weyland-Yutani, not to mention the events of the film's prequels, gives the company decades, possibly, to have deciphered the true nature of the signal despite it being of alien origin.
(at around 1h 35 mins) When trying to abort the countdown, the cancellation instructions Ripley follows with her finger are actually just a French translation of the detonation instructions she followed earlier.
(at around 10 mins) 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.
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.
Despite the humid temperatures of the ship during the detonation sequence, and the fact that Ripley is seen coated in sweat, including her nails, when she disrobes in the escape shuttle, there is no perspiration anywhere on her under garments, not even the armpits.
(at around 28 mins) 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.
(at around 1h 19 mins) The company's orders received by Mother state, "Priority One - Insure return of organism." Although technically synonymous with "ensure", in common usage "insure" is the wrong verb (suggesting that the company should take out a policy with an insurance company). The statement should be, "Ensure return of organism."
Mother's reports of the remaining time in the countdown to self-destruct all say that the explosion will occur "in T minus <x> 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 <x> minutes".
(at around 1h 23 mins) 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.
(at around 1h 21 mins) The milky "sweat" that drips down Ash's forehead before he fights Ripley disappears after he throws her onto the desk. It was not wiped away, because his head is perfectly clean, rather than smeared.
(at around 56 mins) When the alien is popping out of Kane, the camera changes angle and there is a significant amount of blood missing from his shirt. Then when the angle changes again, the blood comes back.
(at around 1h 23 mins) After Ash wrestles Parker to the deck, Lambert runs over, grabs Ash (the prop torso) and throws him aside. In the next scene, Ash is still atop Parker. Lambert then hits Ash with the electric prod.
(at around 1h 23 mins) 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.
(at around 56 mins) 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.
(at around 1h 35 mins) 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." This could be due to sloppy editing, for dramatic effect, or because Mother's voice is not perfectly synchronized with the countdown screen.
(at around 1h 50 mins) As Ripley blows the alien out of one of the Narcissus' aft engines, the exhaust is obviously water because it dribbles down the camera lens. Ridley Scott stated that water was used to create the illusion of plasma. The water flowing over the camera lens is obviously an intended dramatic effect to show the intense energy generated by the intended plasma.
The motion sensor used to track the alien senses micro-changes in air density. They deduce the alien is moving, presumably because of these changes. However, as we can see just before Dallas is ambushed in the air ducts, the tracker does not reveal which level the alien is on as it moves toward him. We learn that Ash's order was to obtain the specimen at the cost of the crew's lives. Therefore, he has intentionally sabotaged the tracker to give the crew misleading information.
Jones vanishes from his carrier as Ripley boards the Narcissus. This is deliberate because the fiery explosion effects used would be too cruel to the trapped animal. However, as a consequence, Sigourney Weaver handles the carrier more roughly than Ripley would if Jones was inside.
(at around 1h 30 mins) The alien's tail snakes between Lambert's feet, but it's not her feet that are shown. Lambert wears cowboy boots; the feet shown wore joggers. The feet and legs were Harry Dean Stanton's (see Trivia).
(at around 1h 23 mins) 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).
(at around 1h 30 mins) 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.