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)
Audio problem: When the T-X steals the car in the beginning, she's driving with both hands on the steering wheel. The car appears to be a 2001-2003 Lexus SC which has a 5-speed automatic transmission (without steering-mounted paddle shifters). However, the sound from the transmission indicates it's a manual transmission rather than an automatic transmission. Therefore, she cannot be shifting gears while having both hands on the steering wheel. (00:07:15)
Revealing mistake: During the opening credits, the Terminatrix steals a woman's car. She uses her mobile phone to dial a number and successfully connect to a computer. However, you can see that the phone has no reception, making a phone call impossible. Battery life is the right hand gauge, and signal strength is the left hand one, with no bars. (00:07:25)
Continuity mistake: When the T-X steals the car in the beginning, she's weaving in and out of traffic and from her view we see that she is coming up to a truck in the right lane. The view changes to view from outside the car and she's turning into the right lane and driving straight ahead. The truck is gone. (00:07:50)
Continuity mistake: When the TX runs a red light in the stolen Lexus, a cop stopped at the red light does a one-eighty to begin pursuit. When the TX pulls over, the license plate on the cop's squad car is not the same as when it was stopped at the red light. (00:08:10)
Audio problem: When the female TX is stopped by police during the intro credits, before the officer speaks you can see the TX's lips moving saying "Is there a problem officer" but her audio is muted. (00:08:50)
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)
Continuity mistake: When the TX pulls up to Jim's Burgers, notice the umbrellas in front of the store and the "in-out" arrows on the road. Asking for Jose Barrera at the drive-through speaker, she drives in and shoots him from the passenger side of the car and exits on the same side of the building she came in. You can see the front of the store with umbrellas upon entry and exit, yet the speaker has disappeared. (00:16:30)
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)
Continuity mistake: After Kate throws John in the dog cage, moments later she returns to say, Mike Kripke's Basement. The first two cutaways to John there are no bars in front of him. On the third cutaway, there are bars. (00:21:05)
Other mistake: When Kate is viewing the T-X on the security cameras, the two views of the corridor do not match each other. For example, the first camera shows glass walls, whereas the second shows wall panels. (00:23:30)
Revealing mistake: When the T-850 drives the truck into the building, from the side view the truck misses the silver car completely. Yet in the next shot it appears to hit it, and the car lurches (somewhat unrealistically as if pulled by a cable) to the left and explodes. (00:24:00)
Continuity mistake: When the T-800 first drives the truck into the Vet clinic, the truck has crashed into the building, so that the doors are inside the clinic. Yet in the very next shot when he gets out, the truck has moved back so that the doors can open cleanly, without the T-800 backing the truck up. Then when John escapes the cage and he runs into the T-800, you can see the truck inside the clinic. It is now more than halfway inside the building. (00:24:15)
Revealing mistake: When the T-X is trying to get Kate out of the car, she rips the door off the truck and pulls Kate out. Kate goes flying through the air and lands on the tarmac. However, if you watch the floor closely just as she lands, you can see that the floor actually wobbles and shakes. It is obviously not real. (00:24:35)
Continuity mistake: When the Terminator puts the tyre wrench in the doors of the van he bends the wrench. But later in the desert it's bent differently. (00:25:15 - 00:41:40)
Continuity mistake: When Katherine Brewster is initially saved by the Terminator from the TX and thrown in the back of the truck, her knees are wet, then drier and drier but then wet again showing the sequence we see was shot at different times. (00:25:30)
Factual error: During the scene where the Terminatrix remotely controls the police and rescue vehicles, we see the police car's shifter drop one notch (from park to reverse) but the car takes off going forward, throwing a cop out. (00:28:55)
Visible crew/equipment: Just before John Connor crashes into the car in front with the Tundra, there are a couple of shots shown from inside. During these shots, there is a cameraman visible on the extreme left hand side of the frame, hiding behind a black jaguar. (00:30:05)
Continuity mistake: When John crashes the Toyota truck into the rear of the silver Taurus, the car's bumper cover lands on the ground to the right of the car, between it and a parked car. When John drives away from the accident, he drives between the Taurus and the parked car, but the cover isn't there to be run over- it's now tucked under the Taurus at the right/rear corner. Then, as the crane smashes the Taurus, the cover is now well to the car's left, in the lane of opposing traffic. (00:31:10)
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.