(at around 27 mins) In the cafeteria, Ripley's glass of orange juice goes from half full to full.
Dillon's glasses disappear after Golic frees the alien. (Assembly cut only)
(at around 18 mins) When doing the autopsies of the Sulaco passengers, Clemens' bloodstain frequently changes.
At the end of the film, Morse is shot in the leg by a Weyland Yutani solider using a pulse rifle. In Aliens, Gorman says that pulse rifles fire explosive light armor piercing rounds which should have blown his leg clean off.
When Clemens pulls the blanket off Newt's corpse in the morgue, Newt's head points directly upwards. In the next wide shot, when Clemens walks away, Newt's head is turned away from the camera, despite nobody having touched her.
(at around 17 mins) When Clemens performs the autopsy on Newt, her blood runs freely as if she had died very recently. However, she had been in the escape pod for a long time and then been frozen in the morgue. Even when defrosted, her blood would have congealed and would not flow or stain clothes the way it does.
If the EEV impacts at a speed high enough to heat up the hull to glow, it would smash up beyond recognition leaving no chance of survival. Even the sheer G-load occurring on impact would be more than enough to kill the occupants, and, if they could be retrieved from the wreck at all, they are liable to have almost every piece of bone cracked to splinters.
The opening caption states that Fury 161 is made for males with an extra Y-Chromosome. XYY, also called Jacob's Syndrome, is not correlated with criminal, violent, or other anti-social behaviors and is this a false stereotype. XYY chromosome carriers tend to be taller than average and may have mild to moderate learning disabilities and lower IQ, but are not necessarily violent or criminal.
(at around 4 mins) As the EEV impacts into the sea there is an oil tanker in the center of the horizon. However, the planet (Fiorina) was clearly rich in oil, as seen when Ripley is rescued from the sea and covered in oil. The tanker could well have been left there from years earlier when the Company was exporting oil from the planet.
(at around 4 mins) When we see the EEV crashing into the sea, the water splashes perpendicularly upwards - which would be impossible as there is strong wind blowing which should have blown the water away.
In the opening, we see a facehugger break through a cryogenic tube and as a result, the facehugger gets cut and we see a small spurt of acid spray onto the floor. The floor then starts dissolving. However, the "floor" is very obviously a piece of styrofoam so that it was easy for the crew to dissolve it with some acetone.
The syringe used on Ripley by the doctor (Charles Dance) is the modern-day Rocket brand from London, clearly shown on the close-up with the Rocket logo and OF LONDON mark.
The prisoner named Vincent is an enigma. He is not present in any scenes before his death scene and seems to just appear out of nowhere.
Ripley goes to some lengths to get Clemens to perform an autopsy on Newt, secretly because she wants to see if Newt was carrying an alien embryo. But why not just use the neuroscanner in the EEV, which Ripley uses on herself later in the film? The autopsy scene is just a contrived way of adding tension.
At 51m 50s the syringe plunger is moving in the wrong direction if he is trying to fill it from the bottle.
When filling a syringe you pull back the plunger to fill the tube with air. You pump the air into the bottle to replace the liquid you then pull out or else you cause a vacuum in the bottle.
(at around 1h 35 mins) After Morse closes the channel door, trapping the alien in the piston chamber, he hollers "I'm going for the lead!" out of sync with his moving lips.
There is no logical explanation for how the Alien egg appears on the Sulaco at the beginning of the film. Although it has been speculated that the Queen Alien laid the egg when she was hiding in the landing gear of the drop ship, the Alien Egg is clearly not inside the landing gear after it has hatched. It appears to be somewhere either inside the drop ship or elsewhere in the Sulaco. Since Queen Alien was never in the interior compartment of the drop ship and certainly never made past the cargo bay of the Sulaco, there is no explanation for how the egg got where it is.
Early in the film the interior of the EEV is a mess, having been smashed up by the crash. However, as the movie progresses, it seems to be in a better and better condition and at the end it seems to be almost intact. It is not a plausible explanation that the interior of the wreckage was cleared up by the inmates on Fury 161 when they were removing the bodies of the rest of the crew and possibly looking for salvage because there is no point that they restore the neuroscanner and the related equipment since (as it is mentioned several times throughout the movie) they have neither the technology nor the knowledge required for any sophisticated equipment.
During the montage at the start of the movie, the facehugger is presented as breaking through some glass followed by spilt acid eating through the decking and causing the cryogenic tubes to be ejected. The broken glass was directly over Ripley, so any acid spilled from the wounded facehugger should have dripped onto Ripley and scarred her horribly if not killed her outright, yet she is uninjured from the facehugger's acid blood.
After Clemens performs his autopsy on Newt for possible Cholera, he states that "There hasn't been a case of Cholera on this planet in over 200 years". The Aliens series is set in the early 22nd century to late 23rd, making the colonization of Fury-161 in the mid to late 20th century, an impossible time frame.
Ripley has Clemens perform an autopsy on Newt, checking for an alien embryo, though she says it's to check for a Cholera infection. With Ripley's experience with this creature, she has already learned that the embryo surviving depends on the host being alive. When Newt drowned in her cryo-tube, the embryo would have died with her. There was never a need to check her body.
When the EEV report is being made at the beginning of the film, Ripley is listed as Lieutenant. Yet, Ripley's rank was always a warrant officer, a lower rank than lieutenant (the extended inquest of the Aliens Director's Cut makes this clear). While it's true that Burke promised her that she'd be reinstated as a flight officer, since they never returned to Earth after Aliens (1986) it is unlikely that this occurred, and certainly not at a higher rank than she was prior to her return to LV-426.
Ripley tells Dylan that she is carrying a Queen, an egg-layer. Having never seen a Queen in its infancy before, and considering the poor level of detail on the ultrasound, there is no way should could have known this. At best it is a conjecture based on the fact that it hasn't burst out of her yet.
(at around 20 mins) In the autopsy-scene Clemens says that "I would consider it unwise to tolerate even the possibility of an unwelcome virus. An outbreak of cholera would look extremely bad on a report." Actually cholera is caused by a bacterium called "Vibrio cholerae".