Factual error: When the T-X is driving the crane and swinging the Terminator around, that is mechanically impossible. All mobile cranes are designed to run only when they are in neutral. The T-X would have burned out the hydraulic pump within seconds. (00:33:50)
Suggested correction: The TX can control other machines including police cars, it's not far fetched she could control and manipulate the crane truck in anyway she wanted.
Being able to control the crane truck does not alter the fact that the hydraulic pump would burn out. That's the purpose of the safety system.
The T-X is a super robot from the future with machine controlling superpowers. So she presumably overrode the hydraulic systems in some techno magical way. None of the Terminator movies are particularly mechanically realistic so this shouldn't shake our willing suspension of disbelief.
I can't answer for every single model of crane as I imagine they all vary, but we have a Demag AC45, a Bocker AK46 or our Manitou 2150. We can operate the hydraulics whilst in motion and we've never once had a problem. That being said, we're not doing 30MPH at the same time as using them, might very well be a different story if we were.
Visible crew/equipment: During the "target acquired" chase scene when the red pickup truck flips over after going through the split semi-trailer there is an overhead shot shown of the action. The next shot when the T-X looks in her rear view mirror at the action, the camera crane that filmed the previous overhead shot is visible in the background. (00:32:25)
Continuity mistake: The driver side rear view mirror is broken on the police car as it chases the tundra truck onto a front yard, but after leaving the yard the mirror is back intact. (00:34:55)
Continuity mistake: During the big chase scene (a little after the Terminator collided with the fire truck), the crane crashes through another glass store front. When it emerges and turns, the hook is tied to the front of the crane, just as it was when the T-X first got it. (00:36:30)
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)
Continuity mistake: When the TX's crane is pulling away after destroying the building facade, it is seen from the high angle that the top of the cab is clean. When the crane is shown again the cab roof is covered in cables and other debris. Also note it remains this way until catching up with Connor in the Tundra truck and then the crane is clean like it was run through a car wash.
Revealing mistake: When the Terminator uses the the G-36 assault rifle, the muzzle of the rifle is fitted with a maneuver ammunition device which shows that he uses no real ammunition, but a variety that just makes "bang" sounds without a bullet. (00:55:35)
Continuity mistake: When the Terminator is hitting the T-X with the fire extinguisher, she puts her fist up and punctures it so the Terminator chucks it down on the floor. We see it on the floor again, but when the Terminator is running towards the T-X you see where the extinguisher was but now it has vanished. (01:18:55)
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)
Continuity mistake: During the shooting scene at the cemetery, note one of the stones (rectangular from the left) behind T-101 when he comes out carrying a coffin. You can see it has 5 holes - 3 left, 2 upper right side. However, a few seconds later, it has 6 holes, but their position has completely changed, 3 upper side, 3 right side. (00:55:25)
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 Terminator is at the AM/PM, he is filling a small basket with various food items. One item in particular was a large bag of chips. The contents in the basket change from shot to shot, most noticeably the chips disappear completely. (00:42:35)
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)
Revealing mistake: During the big fight between the two terminators, the male grabs the female and smashes her head into a toilet. If you watch carefully as soon as her head hits the toilet it cuts seems to cut to another shot. (Easier to see in slow-motion).
Continuity mistake: When Kate takes a gun out of the coffin at the cemetery, you can see she puts her finger on the trigger. In the next shot, her finger is back around the handle and not around the trigger.
Visible crew/equipment: In the scene where John, Catherine and the Terminator are in the mausoleum getting the guns out of the casket, you can see two "marks" taped on the floor in front of John and Catherine. (I think they were red and green). (00:49:55)
Continuity mistake: The amber parking light lenses on the hearse are mismatched and change several times thoughout the hearse scenes (note the Cadillac crest on the left side lens).
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 Terminator jumps onto the roof of the truck that John is driving, the damage he causes changes when we see the truck driving off into the distance. (00:37:30)
Continuity mistake: During the crane chase the amount of damage to the van changes drastically throughout the chase. (00:33:35 - 00:35:00)