Every kid in an action movie is annoying. John Connor who is supposed to be 10 years old in the movie), acts s more like an adult in some ways as a result of his *unorthodox* upbringing. And whenever we see a young kid acting more mature than what we would expect; we tend to get annoyed. We also get annoyed whenever we see kids acting like kids. You just can't win if you're going to have a young kid in a movie.
Either way, that movie was way ahead of it's time. T3 was a good popcorn movie and I happy pretending that T4 doesn't exist.
As for the first one. I might be in a minority who thinks that movie has actually gotten better with age. I didn't appreciate as much when I was younger (though I still liked it), but I really like the dark film noir-esque grittiness. Though I think T2 is overall the better movie; I think that T1 is what really showcases James Cameron's talent like nothing else in his repitoire. Given what he had to work with (T1 was a low budget movie for those who don't know), he really knew how to use the atmosphere and the music to carry the movie when the special effects wouldn't cut it. It's proof that real creativity thrives under constraints.
Another thing I want to touch on is the the Terminator Theme. So simple, yet powerful. I feel like it tells you everything you need to know about those movies. And I wonder why there are no powerful or moving themes like that for newer movies. The recent Batman series was great, but can you remember the theme? Did it even have one? I still remember the 1989 Batman theme and that was awesome, and I wouldn't have held it against Nolan if he had carried that over to the newer series. I honestly can't think of the themes to any newer movies except for Lord of the Rings, and that's over 10 years old now.