Revealing mistake: When Anya sings her song about how she will become Mrs. Harris, she spins Xander's chair around after putting a blanket on him. When she is also sitting on the chair, and you see an overhead shot of them both, you can see a section of the stage floor rotating beneath them keeping the chair spinning.
Continuity mistake: In the flashback to St. Petersburg, 1905, just after the burning man runs out of the room, Halfrek mentions the Revolution. Between shots, Anya's champagne glass switches from her left hand to on the table and back.
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