The character of Reese in particular is very well crafted. A homeless Vietnam vet that you might find in LA in the early eighties. Totally paranoid, totally disconnected/alienated from "modern" society, equipped for a time and place that is totally disconnected from the world he is dumped into. There is a dialogue about institutional failure woven throughout the film: the cops (I'll point out: Arnold executes an entire police station full of cops in this film! Can you imagine that on screen today?) and especially the psychiatrist. Totally incapable of dealing with the demon that haunts the main characters.
There is a dialogue about heroism -- John Connor is apparently a hero, but none of the characters actually feel heroic, they're all just terrified, haunted, and helpless. There is this incredibly "important" thing (the war) but none of the characters actually feel it that way, nor does society. The portrayal of LA -- the cops, the gritty alleyways, the nightclub, the crappy motels... it's LA as experienced by a Vietnam vet.
The first Terminator movie stands head and shoulders above all others in the franchise. It's a truly incredible film and far underrated critically, I really recommend re-watching it with this in mind.