You could look at it as if the John Connor in T3 is in a different timeline than the John Connor in TSCC (and i've gone crosseyed)
Any way there will be no more inconsistancies with TSCC as it has been cancelled. No more Cameron in her underwear.
It's also said in T3 that the events of T2 happened when John was in 8th grade, that would make him 13 or 18, but T1 happened in May, placing John's birth in February, and T2 happens in Summer time (don't ask me how I know), so that would've made him 14.
Also, T3 shows Sarah's birth date as 1959, making her 24 in T1, even though she's 19, despite her being said to be 29 in T2 which happens 11 years after T1.
Also, T1's introduction says the final war happens in 1984. Of course that is not the case. Similarly, T2's intro only states 2 assassin's being sent back in time.
Another weird thing is why after 11 years after the events of T1, there is still just the original terminator as their only weapon? Surely they would've discovered and developed a hell of a lot quicker.
The technology Skynet used was much more advanced than the technology Cyberdyne were using in the 80s/90s. Cyberdyne used reverse engineering, which can take time to process. To discover the unknown data and technology Cyberdyne would have had to analyse the structure, function and operation of the chip from T1.
"It was scary stuff, radically advanced. It was smashed... it didn't work. But it gave us ideas. It took us in new directions... things we would never have thought of. All my work is based on it." - Miles Dyson
Is the fact that Arnie appears as a cybernetic organism surrounded by living tissue in the first, second and third Terminator not an inconsistency? Think about it...
The Terminator is an infiltration unit, designed to "blend" in. How are five "Arnold" style Terminators meant to blend in??? Or 10 for that matter? Once Skynet releases an "Arnold" style Terminator, Skynet cannot really release another, the resistance would know about it. And when another Arnold Terminator does turn up after a group of resistance fighters have dusted a previous one, they'll just go "Look, it's that bloke with a dodgy foriegn accent. Terminator!"
I have thought this through, and Skynet would probably release a Terminator of the same model to different resistance camps. But why would it use the same looking Terminator to infiltrate these camps? Surely it would send a Cameron style Terminator to infiltrate one unit, a Cromartie style to infiltrate another. Etc etc. Therefore there should only be one of each looking Terminator, not 15 or so.
I think John has a conection to that terminator so maybe he picked it the arnie model and sent it back in T2 and in T3 it was the arnie model that killed john in the future cause skynet knew they would have an emotional connection, so katherine sent that terminator back to protect them.
The biggest inconsistency for me is the fact that in T1 its explained that only organic material can come through - that's why they come through naked.
But then how does a big hunk of metal like a T-800 come through? And if you can send some massive amount of metal through simply by covering it in a skin of organic material, why not send weapons through with the T-800? Then he could have his phased plasma rifle in the 40 watt range.
Cameron makes a lame attempt to address with this exchange between Kyle and the doc:
Kyle Reese: You go naked. Something about the field generated by a living organism. Nothing dead will go.
Dr. Silberman: Why?
Kyle Reese: I didn't build the ****ing thing!
Dr. Silberman: Okay, okay. But this cyborg, if it's metal...
Kyle Reese: Surrounded by living tissue!
But even if we accept that - it still doesn't explain why the T-800 couldn't bring weapons with it the same way.
Good point deepstructure. Because presumably a "phased plasma rifle in the 40 watt range" would be made out of metal. Why not just cover it in the same living tissue that the Terminators are surrounded by, right? You would think both things (Terminator and the rifle) would be made of similar material.