Deliberate mistake: While it is established that Angel doesn't age, it's obvious across both Buffy and Angel that David Boreanaz gets older. More unavoidable than deliberate, but still worth noting.
Deliberate mistake: Though vampires are said to possess super-human strength, and are in fact demonstrated to have it, they are often kept confined by the flimsiest of restraints. One distinct example is in season 2 episode 9 when Kendra locks up Angel he is unable to break out despite being held in by nothing but a flimsy padlock. This mistake is pointed out in the DVD commentary as an unavoidable 'mistake'.
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