The showing of the war was ok, but the utter lack of a plausible explanation of how Skynet could even exist after T2 sinks everything.
That's it, in a nutshell. It is no longer a continuous story. T3 messed up the continuity, and they only did it to make the film an action film with a female terminator and newly developed CGI techniques which were made available. The missing story (Skynet of the unchanged future decimating humans, and fighting the Resistance) has yet to be told. We needed to see the story of how the first and second terminators went back to the past, and how they were programmed by Skynet. How were they built? How was the Resistance fighting against them? T4 tried to do that but they ruined their chance by adding even MORE implausible stuff and giving Skynet a face and a place.