Never Kill A Boy On The First Date - S1-E5
Other mistake: In the famous scene where Buffy tells Giles, "If the Apocalypse comes, beep me," she grabs her pager from out of shot. Trouble is, she's standing in the middle of her hall and there's nowhere she could have picked the gadget up from. (00:21:00)
Answer: She has superpowers, ergo fast movement. The reason she outruns him so easily in "Touched" is that she stops trying to actually fight him and just dodges instead.
Shay