Continuity mistake: We see Xander lying in bed with his chest and stomach uncovered. But when Anya comes in and starts talking to him about checking in at the unemployment office, his bed sheets are suddenly pulled up covering his chest and stomach.
Plot hole: Willow hacks into The Initiative's computer system and discovers air ducts and electrical conduits leading to Adam behind 314, but the room doesn't show up on the schematic. It seems unlikely that nobody who didn't know about Adam would have noticed this and investigated.
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