Continuity mistake: When you see the attack aircraft flying towards the planet from the front you can see the pilot Ferro in her dark glasses sitting on the right side of the cockpit, but in all the other close up shots she sits on the left side with Spunkmeyer behind her on the right.
Continuity mistake: Hicks has a heart painted on his armor with a latch locked by a padlock. When Hicks and Ripley enter the elevator after losing Newt, the padlock is missing. After the Alien attack, the padlock reappears.
Continuity mistake: When Bishop is doing his knife trick on Hudson, his hair changes significantly from one shot to another, especially on the top and around the ears. In addition, at the end of the scene, Hudson is given a meal that was taken off a heater nearby on the table. That meal was apparently not placed back for some of the closeup shots, as it is missing from the heater. Finally, the time shown on Bishop's wristwatch seems to change radically about half-way through the scene.
Continuity mistake: When Ripley and the marines go to where the colonists are, there is a ladder in front of the vehicle that was driven inside; the ladder would be in the way if the vehicle was driven further in. But when all hell breaks loose and Ripley decides to drive the vehicle further in, to rescue the marines, the ladder is gone - in fact, a lot of things look different the second time round.
Continuity mistake: Just before the marines are extracted, Hicks tries to close the APC door. An alien stops the door and tries to get inside. Hicks picks up his shotgun and jams the muzzle into the alien's mouth and fires, killing the alien. The alien falls away, they immediately close the door and the APC begins to back up. The camera shot changes to an outside view of the APC. If you look at the area as the APC backs up, you'll see falling debris but no dead alien. It's doubtful the marines would've pulled it into the APC as we don't see it again, or that they would've kicked the corpse out really far due to the acid.
Continuity mistake: In the shot were Ripley is driving the crew away from the aliens, note the big dent in the vehicle. Then in another shot when they finally get outside, there's a shot from the side and the dent is gone. (01:19:15)
Continuity mistake: When the marines first encounter the Alien hive in the reactor, and Ghorman asks Hudson what he's seeing, we're treated to a shot of Vasquez' helmet cam, and her name in the bottom right is missing her first initial. [Timecodes are from the special edition of the movie. The first one is the one for the error, and the second is a different scene with the initial present for comparison.] (01:04:00 - 01:20:00)
Continuity mistake: When Ripley is giving Newt the cup of hot chocolate the handle is on Newt's right. When it shows the close up shots, the handle is on Newt's left. (00:48:40)
Visible crew/equipment: In the scene where Newt and Ripley are trapped in a room with two facehuggers, Newt traps one with a table, and you can briefly see the operator's hand manipulating the legs.
Continuity mistake: Towards the end of the film where Ripley and Bishop are in the dropship flying towards the atmosphere processors, Ripley begins to build a composite weapon from a flamethrower and a pulse rifle. She pulls a flamethrower from a rack on the wall, but lays pulse rifle on the deck of the ship, and then pulls a pulse rifle from the rack and lays a flamethrower on top of the pulse rifle. (01:49:05)
Continuity mistake: In the original "Alien", Ripley dons a space suit in the shuttle, in preparation to decompressing the quarters to the hard vacuum of space. The helmet has no light on its top. Subsequently, in "Aliens", the opening shots pan through the shuttle chamber, and Ripley's helmet sits there...with a light on its top.
Continuity mistake: In the scene where the drop ship is about to leave the main ship look at the picture on the side of the ship, just to the left of the pilot's window. There is a symbol of an eagle. Note which way it is facing. Later when the ship is on the planets surface and the marines are leaving it, the eagle is facing the other way.
Continuity mistake: When Newt is caged in the resin, the cloud of steam around the egg completely disappears when Newt is seen from the p.o.v. of the egg.
Continuity mistake: At the start of the film when you see Ripley in her stasis capsule the glass is clear, but when the salvage men enter the shuttle craft the glass on the capsule is covered in frost which one of the men has to wipe away in order to see her face.
Continuity mistake: Pulse rifles have 10 mm caseless ammo, but if you watch the scene where Vasquez depletes her rifle and then switches to the pistol, there clearly are shell cases being spat out.
Audio problem: In the beginning of the scene where the soldiers are eating in the mess hall, the soundtrack of background noise is played, then repeated.
Continuity mistake: Right after Ripley is rescued from the Narcissus, look at her hair in the clinic. At first there is a wide angle shot of the nurse coming over to her with some small talk. Then, when the shot changes to a close up of Ripley and the nurse, her hair has puffed out about 2 inches more. (00:05:40)
Visible crew/equipment: Just after Ripley drops the first flare (on her way back to rescue Newt), the shadow of a crewmember is cast on Ripley's back.
Continuity mistake: After the Alien Queen is sucked out of the airlock, Ripley climbs back onto the platform and closes the doors. In a shot from above, her left leg has not yet crossed the mouth of the opening. Cut to a closer shot and half her body is already on the platform.
Continuity mistake: When Ripley enters the hive, right before she lights the second flare, she fires a flamethrower burst. When she does, the starter flame goes out, then in the next scene it is on again. (01:53:50)
Answer: It really was all down to James Cameron having already written the script and proving himself capable of directing with 'The Terminator.' It was just a quicker, easier, and almost certainly cheaper decision to let him direct his own script rather than get someone else, even Ridley Scott. While the producers had wanted to make an 'Alien' sequel almost immediately, at the time the head of 20th Century Fox didn't want to pursue it fearing it would be seen as an obvious cash-in and flop. When a new executive at the studio came in a couple years later, the project was put back on track, and I believe Cameron was the first to be approached to write the script.
TonyPH