Continuity mistake: When smashing the truck in the hangar, the T-850 hits it and it falls down so that the bumper is on the floor. When it shows the T-850 from John's POV, the truck is back up on its wheels, although the wheels are still damaged. (01:29:05)
Continuity mistake: When John and Catherine are in the hangar at the runway, the Cessna's tail number is N3035C. When the plane is shown in the air, the number is N3973F. When they land, the tail number has changed back to N3035C. (01:22:25 - 01:25:50)
Character mistake: When the Terminator scans the doorman at the bar, a display comes up categorizing each piece of the doorman's clothing. The word "briefs" is misspelled "breifs". (00:13:40)
Character mistake: In the opening narration, John Connor says that he was attacked by the T-1000 when he was 13 years old. This is wrong. In Terminator 2, we see that John Connor is only 10 years old, as shown on the police computer when the T-1000 accesses it. (00:02:20)
Continuity mistake: In the scene were John, Kate and the Terminator find the RV, when John says to Kate, that Scott's death wasn't her fault, she is sitting in the passenger seat of the broken down Hearse. Then in the next shot Kate completely disappears and reappears when the Terminator mentions the TX is going to kill Robert Brewster.
Continuity mistake: In the cemetery scene when the Terminator uses a bazooka to fire a missile at the TX, the shot that shows the TX being launched up in the air and hitting a gravestone should have shown the car used by the TX and the road where the car was parked. In the next shot, when the TX gets up and starts to run after the hearse, the road reappears but not the parked car. (01:04:40)
Continuity mistake: In the scene just after Kate Brewster's dad has been shot he says to go to his office. On the way there you can see his jacket is undone and you can see his shirt and tie. Yet when they enter the office it shows him sitting down with his jacket neatly buttoned up. For a guy who just got shot and is running from machines, I doubt he would worry about buttoning up his jacket. (01:16:40)
Continuity mistake: JC's leg was crushed by the T-X. After emerging from the elevator, he limps on the wrong leg. (01:36:00 - 01:36:55)
Revealing mistake: When John, Kate and the Terminator are in the Winnebago, there is a shot that's facing Kate where John says to her that they're going to pull the plug on Skynet and that the bombs won't fall. In this shot, look at John's hair. The green screen is reflected onto it. It is visible throughout the rest of the scene. (01:09:45)
Continuity mistake: When the T-850 walks around at the gas station, shopping, he fills up the shopping basket, and one of the bags of chips can't fit in the basket. However in the next clip, the basket is half empty and there is plenty of room for the two boxes of candy he grabs at the counter. (00:41:00)
Continuity mistake: As the hearse comes out from under the truck while they are trying to get rid of the Terminatrix, you can see that the windscreen is intact. But as they drive down the hill it's missing. (00:59:10)
Continuity mistake: When Kate gets the phone call in the middle of the night to goto the pet clinic, her phone is a white+blue Nokia 8310. Later on when she is calling from the back of the pet truck and it loses reception and the camera goes onto the phones, its now an all blue Nokia 51xx (I think) series phone. (00:17:30 - 00:29:25)
Factual error: When Catherine's father walks through the corridor of the military base, on his way to the first test of the flying Hunter Killers, he is accompanied by a female civilian employee who is wearing a yellow blouse and you can see a fair bit of cleavage. Civilian employees on US military bases are required to dress modestly, and she is showing too much cleavage. The US military is utterly rigid in imposing their dress codes on civilians and she'd be ordered to button up.
Revealing mistake: When they are driving the tundra after the big champion crane crashes, the Terminator gets in the truck. If you look closely, the truck's shifter is all the way in park. (00:37:55)
Continuity mistake: After the first two fireman jump out of the fire truck, Arnold climbs in and says "Get out" to the other fire fighters. When the next two fireman jump out, the first two are not seen on the road behind them. Also, when Arnold changes gears on the fire truck none of the four fire fighters are seen on the road. (00:36:10)
Visible crew/equipment: Right after the ambulance runs over Arnold's motorcycle a shot of him hanging on the crane hook is shown. You can see the safety cable attached to the left of his belt. (00:33:25)
Factual error: When Arnold is done shooting at the cops in the graveyard scene, there are birds singing in the background. No way that any birds would be left in that area (not to mention singing) after at least 15 machine guns have been firing for more than 2 consecutive minutes, not to mention the cop car exploding. (00:55:50)
Continuity mistake: When the remote cars are crashing into John Connor's truck the up close camera angles do not show the same damage on the front and sides of the police cars as the far away angles do. (00:32:40)
Revealing mistake: During the entire hearse chase scene, the transmission shift lever is in park. (00:55:00)
Suggested correction: This isn't a plot hole. It's just your unfounded assumption. There's no evidence to support the supposition that the T-X has such audio detection capability.
Even if she could detect it, how could she discriminate between the sound of Catherine breathing and that of the dozens of caged animals in the room? That's stretching even fictional technology a little far.