Who, or what, is the Terminator?
A Terminator is a cyborg or "cybernetic organism" composed of a hyper-alloy combat chasis covered in living tissue. Terminators (in their endoskeleton form) were originally designed by Skynet during the early days of the war with humanity for the purpose of carrying out the ground war against the remaining human forces. Being of roughly equal size to human targets and with similar mobility, terminators were able to follow humans where the larger HK (Hunter-killer) tanks and hovercraft could not.
Who, or what, is Skynet?
Skynet, despite being largely unseen, is the primary antagonist of the Terminator series. It is an artificially intelligent computer network. Reese explains that Skynet was built for NORAD (North American Aerospace Defense Command), which was America's primary defense during the Cold War. It is stated that it was built by Cyberdyne Systems.
How is it possible that (future) John Conner was able to send Reese back in time to prevent his mother's death and become his father?
While this conundrum is widely believed to be a plot hole in the story, it is actually indicative of the paradoxical nature of time travel itself. The "Connor Paradox" is best explained via the Novikov self-consistency principle of time travel.
Why does The Terminator ask the gun store proprietor for a Phased Plasma Rifle in the 40 watt range?
This was most likely an error or omission in Skynet's programming of The Terminator - directed energy weapons had not yet been invented in 1984.
How is the terminator able to go back in time via the time displacement machine if it only allows living organisms?
As stated by the character Kyle Reese, the Terminator is covered in living tissue, allowing it to go back in time as a living organism.
Couldn't Sarah and Kyle have tried to prevent Skynet (and the Terminator) from being created?
This was actually part of the original shooting script. A scene was filmed in which Sarah traced the creation of Skynet back to a company called Cyberdyne; she suggests to Kyle that they go there and stop Skynet from being made. This would also eliminate the Terminator from existence. But Reese refuses, saying his mission is to protect her, not alter the future, which leads to a confrontation between the two that ultimately results in Reese suffering the emotional breakdown of being a man out of time.
If The Terminator is an infiltration unit who can mimic voices, why does it speak with a thick Austrian accent?
The obvious answer is that's how Arnold Schwarzenegger talks. A movie answer is that the Terminators capture humans, replicate their flesh/likenesses and voices in order to be better at infiltrating. So however the captive they replicate spoke, that would be their default voice pattern.
Tanker truck obviously being towed, the wire pulling the tanker truck is visible several times.
As the tanker truck is pursuing Sarah near the end of the film, the parked car that the truck smashes is already badly damaged from a previous take.
Obvious stunt double for Reese when the Terminator punches him on the catwalk.
Obvious stunt double for Kyle when he and Sarah are switching sides in the pick-up truck.
Obvious dummy for the Terminator when he is sliding on the asphalt after getting hit by the pick-up truck.
When the Terminator's flesh is burning off, a wire is clearly visible moving the Terminator puppet around.
At the factory, when Reese is attempting to damage the terminator with a metal rod, one of the shots reveals an obvious stunt double.
When the black pickup rolls over, it is obvious that it has no engine, transmission, or driveshaft.
Obvious rubber mask when the Terminator has cut out his eye and sticks the towel in the eye socket.
The position of "Pugsley" while Sarah listens to the telephone messages.
The police clerk looks up from his desk to see headlights coming at him. When we see the front of the car, the headlights are off.
The black pickup truck that Sarah rolls onto its roof appears soon after undamaged.
The terminator's supposedly cut-out eye is visible through the sunglasses.
In some scenes, Reese has a clean shaven face. In others, he looks like he's growing a beard.
Position of Sarah's right hand (on Reese's cheek) before she starts kissing him and when she is kissing him.
The burning cab that the Terminator jumps out of is not the same type as the one he jumps into.
The bandage on Reese's right hand disappears when he and Sarah climb into the black pick-up truck.
The broken window in the Gray Ford changes sides during the movie.
The second Sarah killed is given the full name of "Sarah Louise Connor". However, she is listed in the phone book as Connor, Sarah Ann.
When the Terminator is using the knife to cut away his eye, from the side view, there is no blade in the knife.
In the chase with the gray Ford LTD, dents, and hubcaps appear, disappear, and reappear on the vehicle throughout the chase.
In Technoir scene, the music changes during one cut between phone conversation with answering machine.
Amount of time between Sarah dialing phone at Technoir to the time of answering machine pick-up.
At the end of the film, the paramedics load Sarah into the ambulance feet first. Paramedics always load a victim's body head first.
When Sarah Connor uses the pay phone to dial 911, she puts a quarter into the phone before dialing. 911 is a toll-free call. However, one could say that she would have been too frightened under the circumstances to remember that.
May 12th in 1984 was a Saturday not a Friday.
Errors made by characters:
(possibly deliberate errors by the filmmakers)
When the Terminator is heading into the gun store, there is a sign on the glass that says "Clearnce Sale".
When the Terminator is shooting Ginger, he can clearly be seen closing his eyes with each shot. The flash of the gun should not affect the Terminator.
A "phased plasma rifle in the 40-watt range" wouldn't do very much damage. It has the power of an ordinary 40-watt light bulb found in any household.
The sound of the car window being smashed by the terminator.
During the police station shoot-out, the terminator uses a shot-gun but it makes the sound of an automatic weapon.
When Sarah is walking from her apartment you can hear the heels of her shoes hitting the pavement. Later when she's walking into the disco she's wearing tennis shoes.
When Sarah realizes that despite being burned, the terminator is still alive, you can hear her screaming "No, no!". It's obvious that she's not actually screaming the second "No!"
Crew or equipment visible:
When the Terminator is rising to his feet after getting blasted out the window, a production vehicle and a huge stage light are visible behind him.
When the H-K is pursuing the car, you can briefly see a semi trailer in the background. Possibly a production vehicle.
A stage light is visible in the background when Reese is in his crouch after arriving from the future.
When the Terminator finishes punching the hole in the door to the computer factory and walks in, a puppeteer's head can be briefly seen behind him.
In the future scene where Reece and other fighters are just entering the underground 'base', you can see a camera crew off to the left as the scene pans out.