Audio problem: After Bond sets the timer on the bomb at the end, the ticks don't add up. There's a definite tick each second, and you can count 12 of them after he starts it, then we cut back to the bomb and only 7 seconds have passed. (As a vague trivia aside, coincidence though it is, on the UK DVD he pulls the pin out at the DVD second timer ticks onto "07").
Audio problem: After the bus crashes to a halt on the courthouse steps, the gunfire stops. A few seconds later, a bullet hole opens up on the side of the bus - but there is no sound.
Audio problem: The rock drummer is way out of sync with the drum sounds. Examples include fills, rolls, and cymbal crashes being performed when a straight beat is heard. (01:34:20)
Audio problem: During the scene where Lauren is talking to Wade on the phone and the car smashes through the window, she says she's hears the engine of the car, and that it "sounds so weird". Watch closely, though, and you'll see that the words aren't quite synchronized with the way her mouth moves. (I saw this on the VHS tape and the DVD).