Homecoming - S3-E5
Continuity mistake: In numerous episodes, including 'Homecoming', we see vampires being killed when they weren't stabbed through the heart (the Texan girl vampire in this episode is stabbed practically in the stomach). But the show also makes an issue of the fact you have to stab a vampire directly in the heart to kill it (think the flashback in 'the Becoming, Part 2' where Buffy misses the vampire's heart, or 'Pangs' where Spike gets staked several times).
Homecoming - S3-E5
Visible crew/equipment: When Buffy and Faith are in the library, a person's arm wearing a white shirt can be seen on the left side of the screen behind Buffy in one shot.
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