I Only Have Eyes For You - S2-E19
Factual error: In the episode 'I Only Have Eyes For You', during the flashbacks to 1955 James and Grace dance, and James later shoots himself, to the song 'I Only Have Eyes For You', which wasn't released until 1959. (00:18:20 - 00:26:50)
Factual error: When Angelus is torturing Giles in this episode he is seen with Giles' glasses, and he cleans them by breathing on the glass and wiping with a cloth. Vampires don't have breath, as Angel tells Xander in 'Prophecy Girl' from season one - even if he can force some air out of his body, it wouldn't be warm, moist air, which is needed for condensation to clean glasses with.
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