Revealing mistake: When Arnie hits the telegraph pole with the red sports car, you can see Rae's "dummy" head go flying off over the windshield (00:40:18)
Factual error: Matrix reads coordinates N33° 13' W117° (or possibly W119°) 18'. Neither LAT or LONG has seconds; just degrees and minutes, but he says, "These coordinates are somewhere near Santa Barbara". Even if you fill in 59" for the latitude north, it's still quite a ways south of Santa Barbara. If you fill in 119° it takes you farther west out to sea: that much further from Santa Barbara. The closest island to those coordinates is San Nicolas Island, and since they did go to an island later, that must have been it. Still a far cry from Santa Barbara. The handwritten coordinates would be much easier to read on Blu Ray. (00:52:10)
Factual error: The gun that Arnold uses at the end to take out a hundred soldiers would need to be deployed. The kickback would knock even Arnie flat on his back after a few shots fired. And there is no way he could run and shoot at the same time. (01:12:40)
Continuity mistake: When Matrix boards the plane towards the beginning of the film, it is early evening - the sun is shown to be low in the sky, casting long shadows. Once he has escaped from the plane and is making his way back across the runways into the airport building, the shadows are smaller and more intense, showing the sun is more directly overhead - therefore it has suddenly become much earlier in the day. (00:21:50 - 00:24:15)
Continuity mistake: When Arnold is crashing into the gun shop in the caterpillar you can see the camera to the rear (a black round one) and then also the camera at the front can be seen as a yellow box, attempting to be disguised as part of the engine block. These quickly disappear in subsequent shots.