Continuity mistake: When Dawn is in Principal Woods' office to talk about the accident, she gets up and leaves. Her bag is still hanging from the chair, but she has it in the next scene.
Visible crew/equipment: During the scene where Willow and Anya fall in love with RJ after he visits Buffy's house, and everyone but Dawn runs off to do their thing, the camera pans to Dawn and a woman with a maroon, long sleeved shirt is briefly visible standing on the stairs to Dawn's right.
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