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)
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)
Audio problem: While the T-101 takes off the crowbar at the gas station it makes a clanging sound before it even leaves his hands. (00:43:15)
Audio problem: When Arnold makes the slow turn at the cemetery from Dr. Silberman's view, he starts firing his weapon at the police but we don't hear it. In the very next shot, he repeats the same action but we hear it this time.
Answer: He didn't program the Terminator, she did - remember, John is dead, successfully eliminated by that very Terminator. As to why she didn't program the Terminator to obey both of them, that's an open question - possibly she needed to supply a voiceprint which obviously couldn't be obtained from the deceased John (which would also explain why the Terminator in T2 appeared to only be programmed to obey John, not both John and his mother). Alternatively, it's plausible that the Terminators can only be programmed to obey one individual, in order to prevent problems in the case of conflicting orders.
Tailkinker ★