Continuity mistake: At the hospital, a guard opens a door with his club, takes it away and looks inside. From a different angle the club is still on the door.
Continuity mistake: When Dyson enters the vault, the door is open different amounts between shots.
Continuity mistake: The position of Sarah's left hand clenched on the playground fence is higher-than or parallel-to her right hand, depending on the angle.
Continuity mistake: When the Terminator arrives on earth, his position differs between the first and second shot, with his left leg protruding more/less and his back crouched/slightly raised.
Continuity mistake: When the Terminator's chopper breaks through the gates of the reservoir, they sound as if they crash against the fence, yet a frame later, from the angle in front, the gates are open wide and still.
Continuity mistake: John enters the canal, passes by a bridge and pulls over 200 meters ahead. From his POV, the distance from the bridge is merely 50 meters. (00:35:00)
Continuity mistake: During the pool fight scene, you can see there's an orange ball next to the upper left pocket. In following shots it's no longer next to it and it has a dark ball in front.
Continuity mistake: At the steel mill, the T-1000 points his finger at Sarah and tells her to call John. The style and position of the loose hairs around her forehead change between frames.
Answer: Skynet became self-aware at that time, but didn't launch the attack until the humans got scared and tried to pull the plug on Skynet.