(at around 41 mins) The timer on the bomb says 12 it ticks down to 7. Seven audible ticks later it says 3 seconds left.
The bomb shows 12 seconds left, beeping once per second it counts down to 10 seconds. When the shot cuts it's back to 12 seconds again and beeps enough times to indicate the bomb would be detonated but the following cut shows there are still 5 seconds still remaining. Then the beeps indicate the bomb should be at 1 second but when O'Toole goes to diffuse it there are still 3 seconds remaining.
When the "battle of the Hellmouth" begins in the library, the handles abruptly disappear from the library side of the doors, obviously for safety reasons necessitated by the upcoming wire gag where Buffy is slammed through the doors into the corridor beyond. Also, the cylinder lock on the outside push-plate jumps from below the handle to above it.
Jack has a supposedly razor sharp knife, but he runs the blade side behind Xander's ear and down his neck without leaving a mark.
When Xander drives off with the girl in front of the donut store, the tires on his '57 Chevrolet give off a short squeal. Having an automatic transmission, that car cannot make the tires squeal when setting off, no matter how hard and fast you step on the gas.
During the "battle of the Hellmouth," after Buffy is slammed through the library doors into the corridor beyond, the view cuts to the multi-headed monster following her out and you can clearly see the wheeled dolly supporting the leftmost head and the crew member behind the dolly operating the head. (Hitting pause during the bright flash of light gives a very clear view.)
At 38:14, as Xander comes down the basement stairs, at the top of the picture you can glimpse part of the lighting instrument that is throwing the bright splash of light onto the wall above Xander's head.
At 35:42, as Jack and his gang are running down the street after Xander's car and Jack shouts, "He's heading for the school," everyone in fact is heading *away* from the school, which is visible in the background behind Jack, only a half-block back up the street (and extending all the way down the left side of the street, as well).