Continuity mistake: In the previous episode, Empty Places, Kennedy had a cut across her nose and two more between her eyebrows in the last scene. In the first scene of this episode, which takes place a few minutes later, the cuts are completely gone.
Continuity mistake: This episode takes up exactly where the previous one (Empty Places) left off. Anya now has curly hair, but she had straight hair at the end of Empty Places.
Continuity mistake: Anya's hair changes from straight in the previous episode to curled in this one, even though it is set directly after.
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