1. Apparently, Kyle Reese carries around a shotgun. In a city full of metal walking tanks. That'll be real effective.
Plasma weapons don't exist (yet). and a shotgun beats a crowbar in that it's ranged weapon. And you can load shotguns with solid slugs.
2. How can Skynet see the future/past? Is it because it's made of magic? How does it know about Kyle Reese?
I'd think because Dr. Silberman published all the rantings and ravings that Sarah did when she was under his care at Pescadero Mental Institution in published medical journals as examples of "AWESOME PSYSCHOSIS!" Remember how he was talking to the other shrinks in T2 about how fucking awesome Sarah's psychosis was?
And also because even if 1/2 of all news ever published is destroyed; Skynet is smart enough to set up a section devoted to looking through past history for possible terminator attacks -- remember T-1 and T-2 weren't exactly QUIET; the T-800 in T1 killed a entire police station full of cops; while Uncle Bob shot up an entire parking lot of cops with zero casualties, and then blew up cyberdyne. Lots of eyewitnesses.
Then we have the video footage of Cyber Research System's facility from T3 that Skynet has, of T-850 Ahhhnuld battling it out with the T-X.
EDIT: Plus, we have the video footage of Kyle Reese's interrogation from T1 that no doubt Silberman referenced to and had transcripts made of, to help talk about "Psychosis transferrence" from Kyle Reese to Sarah Connor.
3. Skynet is a complete moron for developing those plasma gun things in T1, given how nothing Connor had could scratch Arnold.
Because it wants something more efficient for killing people with a lot more stowed rounds and less weight? If your T-600 can carry 1,150 rounds on it's backpack with a conventional weapon, and 11,500 rounds with a plasma weapon; which would be more efficient for long duration patrols, with less resupply needed?
4. Why is a submerged submarine transmitting the kill signal, instead of something... you know, not under hundreds of feet of water and operating hidden? Also, why was there an AWACS radar dish thing on top of it?
Hell if I know.
5. Who the heck built all those giant robot arms and stuff in the Death Camp and Terminator Factory? In T3, didn't Skynet just have a bunch of minigun-armed tankbots? How can it build an infrastructure at all?
Remember that by this point it's been 15 years since judgement day -- I'd imagine Skynet started out with some semi-automated factories in non-nuked areas; built some T-2 terminators to round up humans, and used them as slaves to build T-3 and T-4 terminators.
Skynet also had the bonus of knowing exactly what happened on Judgement Day -- the rest of the world, except for John Connor and Katherine Brewster, don't. So the world's militaries, etc, will all suspect it was a American/Israeli/Chinese/Russian etc attack which started the war, not a defense network; so Skynet has time to build up a small base without being under constant attack.
7. Heart Transplant Surgery in a dirty, wind-blown hangar is apparently quite easy.
Hey, don't ask me.
8. Why didn't Skynet just carpet-bomb that little bunker, or all those A-10s sitting open on the tarmac?
Because Skynet hasn't yet developed it's capabilities to the level of 2029, forcing the resistance to go underground even more? At this point, the human resistance can still openly contest a lot of area apparently.
9. Hunter-Killers and the prisoner transport seem to operate off anti-gravity.
You didn't notice the jet engines on the sides?
11. Why didn't Skynet just shoot Kyle Reese? Why take him to the 'overly elaborate and easily escapable death-trap room'?
I think at this point, Skynet had thought things through and concluded that instant "one-shot-I-WIN!" solutions don't work; judging from studying the attempts to send terminators back to get victory. Remember, if Kyle Reese is killed; all John Connor has to do is tell Private Joseph Schmuckatelli that he is to refer to himself as Kyle Reese for "security reasons" when he sends him back to 1984.
It's why I think it did this solution which tried to tie in getting as many of it's enemies: Reese, Connor, the Resistance Leadership, and much of the surviving Resistance itself. Obviously, you can't kill Reese the moment you spot him, because there's always the small chance that Marcus will notice a dead Reese, and send some sort of signal to Connor to not come there, before your hidden programming can take over.
12. Apparently machines, like puppies, make noises to express that they're happy. Only machines go 'BRRZGHH-KRRKGKHHH'.
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WARK WARK