(at around 1h 30 mins) When Ripley tries to break the glass in the med lab there is a scuff mark on the glass before her first swing. After this finishes, the mark disappears and we see Ripley actually making the mark with her second swing. (This goof was digitally corrected for the blu-ray edition)
(at around 1h 45 mins) In the elevator escape scene where Hicks gets acid sprayed, he holds his gun in front of his face and turns his head to the left. Any acid burns he got would have been to the right side of his face. As they fight to remove his melting chest armor, there are no acid marks on his face. When they leave the elevator, the acid burns are on the left side of his head, instead of the right side.
(at around 2h 10 mins) After the Queen falls down the airlock, the sharp end of her tail is missing (obviously unintentional, and overlooked or not repaired by the crew). The tip is back on moments later as she's tumbling through space.
(at around 2 mins) In Alien, el octavo pasajero (1979), the computer displays have an old-fashioned "teletype" clicking noise when they show data on their screens. However, when the screen in the Nostromo shuttle comes to life at the beginning of Aliens, the display looks and sounds more modern like the other computer screens seen later in the film - even though 57 years have passed and the equipment in the shuttle has not been touched all that time.
(at around 1h 7 mins) After an alien smashes a hole through the triangular windshield on the APC during the escape from under the cooling tower the windshield is then shown with an unbroken windshield as it exits on to the planet surface.
(at around 31 mins) When the dropship is released, it is shown to be falling immediately as if in full gravity. However, since the Sulaco is placed on a stationary orbit, the dropship should remain in place upon releasing the clamps. An additional burn would seem to be necessary to initiate breaking orbit. However, a burn is not the only way the dropship could be moved out of the clamps. Other technology could well do it, and might be preferable to a burn that close to the ship. For example using electromagnets to push it. Or artificial gravity may be able to be reversed, or a similar technology could be used create a repulsive force. However, if any of these methods were employed, the separation of the drop ship would have been far smoother than it was and it was obviously an attempt to show it responding to the planet's gravity.
(at around 56 mins) The reason given for removing the marine's ammunition is that the facility is a giant fusion reactor and damaging the cooling system will cause a thermonuclear explosion. A fusion reaction does not use or produce fissionable material so it cannot cause a thermonuclear explosion.
(at around 31 mins) The landing sequence is incorrect. The dropship is seen accelerating while deorbiting, such acceleration would send it to a higher orbit. Deorbiting needs deceleration from the orbital speed. The dropship should have fired retro-rockets or it should have turned backwards to use the main thrusters for deceleration. Moreover, if the Sulaco is exactly above the colony (as stated in the novelization), the dropship should have done a vertical drop (relative to the planet) or should have completed a full orbit while descending to end up right above the colony.
(at around 2h) At the end of the movie, the compound explodes and the survivors escape in a shuttle. We see that brightness of the explosion shines on their face. But in fact, the explosion and the light source is behind, so there's no way their sight would be affected by the brightness.
(at around 1h 50 mins) When Ripley is arming up to rescue Newt, she takes grenades from a case that is clearly marked 40mm. The Marines use pulse rifles with 30mm launchers.
(at around 1h 40 mins) When the aliens capture Newt and Ripley tries to go after her, Hicks holds her back and tells Ripley that they can track Newt using the tracking device. Hicks gave the tracker band to Ripley and didn't witness Ripley giving it to Newt so he wouldn't have known this. However, he didn't witness it onscreen; Ripley obviously told him about it offscreen.
There are several instances in the film of someone shooting an alien at point-blank range, yet not getting any of their acidic blood on them. The pulse rifle rounds are obviously powerful enough to knock the aliens far enough away to prevent the shooter from getting sprayed.
(at around 1h 29 mins) When Ripley goes back to medical to join Newt, she lays her rifle on top of the bed and then lays down on the floor beside Newt. Moments later she looks to break the glass but finds her rifle laying on a table on the other side of the glass. The scene makes it clear that Burke entered while she and Newt were asleep and laid down the opened containment cylinders with the facehuggers inside of them; it's fairly obvious that he moved her rifle out of the room as well (note Ripley's expression when she sees her rifle).
(at around 9 mins) The inquest had gone on for "three and a half hours", yet no one mentioned that LV-426 had been colonized for over twenty years. According to Van Leuwen in the novelization, the committee felt that such information would have biased Ripley's testimony. He doubted that it would have made a difference in their decision and that she still believed what she believed, despite the fact that some of his colleagues were of a different opinion.
In Alien, el octavo pasajero (1979), LV-426 is adjacent to a huge planet with Saturn-like rings (which it probably orbits). Such is its size, it can even be viewed from the surface (i.e. when the Nostromo crew investigate the alien ship). The ringed planet is never seen in this film, either from space or from the surface of LV-426 because James Cameron simply chose not to depict it from any angle.
(at around 2h 10 mins) When Bishop saves Newt from being sucked out of the airlock, part of Lance Henriksen's real torso can be seen beneath the false one, emerging from a hole in the floor. (James Cameron acknowledges this error on the DVD commentary; the goof was digitally corrected for the 2010 Blu-ray release.)
(at around 21 mins) When Bishop is "doing the thing with knife" the scene is sped up to give the impression that Bishop is lightning fast. Apone can be seen rocking his head back and forth, also at a ridiculous speed.
(at around 1h 55 mins) When Ripley turns to find herself in the Queen's chamber, Newt's hand is rigid because she is holding a lightweight Newt dummy.
(at around 56 mins) Gorman states that the M41A Pulse Rifle fires 10mm explosive tipped case-less ammunition, several times throughout the film, you can clearly see casings leaving the ejection port of the pulse rifles. Caseless ammunition, as the name suggests, doesn't have a shell casing to eject; it's an integral part of the ammunition and either exits the barrel along with the round itself or is consumed by the act of firing. This is because the marine's prop weapons were made by combining modified Thompson SMGs and Benelli shotguns, both of which use conventional "cased" ammunition.
(at around 4 mins) When the salvage crew shines a light onto Ripley's face while she is sleeping at the beginning of the movie, her right eyelid twitches. Although people's eyelids twitch all the time when they are asleep, Ripley is frozen in cryogenic suspension - not merely asleep.
(at 10:54 in the director's cut) When Ripley is being questioned by the company officials, the records of the dead Nostromo crew from the first movie are displayed on the screen behind her. Even though these are supposed to be official records, there are frequent typos: In Parker's record, the word "and" is misspelled as "aand" twice, and "throughout" is misspelled as "throuhout."
(at around 20 mins, extended version only) When Newt's mother is calling in the mayday, she is heard saying "Alpha zero two four niner" repeatedly, but the second time she says it her mouth is saying something else.
(at around 1h 40 mins) During the ventilation shaft scene towards the end of the movie Vasquez tells Gorman "you always were an asshole". However, you do not see her lips moving at the end after the camera angle changes.
(at around 1h 6 mins) After the first contact with the Aliens at the processing station and Drake is killed, Vasquez is being held back by Hicks near the door of the APC. He yells that Drake is gone and she says, "No he's not," but her mouth does not move in sync with the line.
(at around 1h 1 min) While Frost is falling after being set on fire and falling over railing, just before the shot cuts away, in the bottom left corner you can see a crewmen moving and a boot sticking out from the shadows.
(at around 1h 55 mins) When Newt is cocooned and Ripley finds her, two suspension lines are visible on the first alien that comes bounding off the walls to attack them.
(at around 31 mins) When the team is descending down to the planet, camera lights and screens are clearly visible in the reflection off Ferro's mirrored sunglasses, and in several shots.
(at around 26 mins) After Spunkmeyer loads the missile, he calls "Clear behind!" and walks the power loader backward. A thick cable can be seen attached to the loader's left foot. (The loaders are supposed to be free-standing.)
(at around 1h 1 min) Before the marines' final stand in Operations, their motion trackers cannot tell if the aliens are on the same level. Therefore the aliens' ability to surprise and slaughter the marines hinges entirely on character error. Ripley references the earlier scene, in which they examined the floor plans, with the possibility that the aliens came in through something they missed or was not in the plans, that being the space above the suspended ceiling vents. By this time, the stress of the situation could have caused everyone to forget this, unlike the calmer floor plan scene.
(at around 13 mins, extended version only) During the inquest, Van Leuwen refers to Ripley's company ID number as NOC14472 while the data screen in the background displays NOC14672.
(at around 1h 21 mins) Burke tells Bishop to keep the facehuggers alive for return to the company labs. Given the harm they would inevitably have caused, complying would seem to be a violation of Bishop's programming. If not, then Bishop is being remarkably candid, meaning Burke didn't tell him to keep that order secret.
(at around 54 mins) When the marines first enter the building, their 'mission time' indicators constantly move back and forward through time by as much as 12 minutes (from 5:21 to 5:33).
(at around 1h 2 mins) When the ammo bag that Frost had been holding explode, Crowe is thrown against a wall, breaking his neck, yet Hicks reports that "Wierzbowski and Crowe are down". He should have said "Crowe and Frost are down", as Wierzbowski is still alive at this point.