When Buffy fights Glory at the Zoo, and later when she returns to the Magic Box, she is wearing heeled boots, but in between, at the hospital, she is wearing jogging shoes.
When Buffy takes off after the big snake she chases it east on Main Street from the Magic Box, but when Giles picks her up in his car she is suddenly *west* of the Magic Box, running *west* on Main Street. They turn south at the end of the street, then the view cuts to them again heading west up Main Street from the Magic Box past the exact spot where Giles picked Buffy up moments ago.
The test that Joyce goes into the hospital for was mentioned as a CAT scan, the device that is used is actually a open MRI. A CAT scan machine actually looks like giant donuts.
During the snake hunt, when Giles backs up his red BMW after first driving past the hole in the fence, he brakes and the sound of his tires squealing goes on for a second even after he has come to a stop.